Ramaré, Olivier
Overview
| Works: | 41 works in 62 publications in 3 languages and 417 library holdings |
|---|---|
| Roles: | Author, Other, Thesis advisor, Opponent, htt |
Publication Timeline
.
Most widely held works by
Olivier Ramaré
Arithmetical aspects of the large sieve inequality by
Olivier Ramaré(
)
6 editions published in 2009 in English and held by 271 WorldCat member libraries worldwide
"This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is squarefree. In the end the problem of equality in the large sieve inequality is considered and several results in this area are also proved."--Résumé de l'éditeur
6 editions published in 2009 in English and held by 271 WorldCat member libraries worldwide
"This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is squarefree. In the end the problem of equality in the large sieve inequality is considered and several results in this area are also proved."--Résumé de l'éditeur
EXCURSIONS IN MULTIPLICATIVE NUMBER THEORY by
Olivier Ramaré(
)
3 editions published between 2021 and 2022 in English and held by 58 WorldCat member libraries worldwide
This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided "walks" invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin-Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at "higher ground" where they will find opportunities for extensions and applications, such as the Selberg formula, Exponential sums with arithmetical coefficients, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area
3 editions published between 2021 and 2022 in English and held by 58 WorldCat member libraries worldwide
This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided "walks" invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin-Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at "higher ground" where they will find opportunities for extensions and applications, such as the Selberg formula, Exponential sums with arithmetical coefficients, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area
Arithmetical Aspects of the Large Sieve Inequality by
Olivier Ramaré(
)
4 editions published in 2009 in English and held by 17 WorldCat member libraries worldwide
This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is squarefree. In the end the problem of equality in the large sieve inequality is considered and several results in this area are also proved
4 editions published in 2009 in English and held by 17 WorldCat member libraries worldwide
This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is squarefree. In the end the problem of equality in the large sieve inequality is considered and several results in this area are also proved
Excursions in Multiplicative Number Theory by
Olivier Ramaré(
)
1 edition published in 2022 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2022 in English and held by 16 WorldCat member libraries worldwide
Arithmetical aspects of the large sieve inequality by
Olivier Ramaré(
Book
)
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
Primes in arithmetic progressions by
Olivier Ramaré(
Book
)
3 editions published in 1994 in English and Undetermined and held by 3 WorldCat member libraries worldwide
3 editions published in 1994 in English and Undetermined and held by 3 WorldCat member libraries worldwide
Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients by
Andrew Granville(
Book
)
3 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Un parcours explicite en théorie multiplicative by
Olivier Ramaré(
Book
)
3 editions published between 2003 and 2018 in French and held by 3 WorldCat member libraries worldwide
3 editions published between 2003 and 2018 in French and held by 3 WorldCat member libraries worldwide
Une région explicite sans zéro pour les fonctions L de Dirichlet by
Habiba Kadiri(
Book
)
3 editions published between 2002 and 2013 in French and held by 3 WorldCat member libraries worldwide
Nous étudions la répartition des zéros non triviaux de la fonction Zêta de Riemann. Plus précisément, nous montrons qu'il n'y en a pas dans la région [...]. Les méthodes élaborées dans ce cas se généralisent alors à celui des fonctions de Dirichlet et nous établissons que les fonctions L associées à un module q fixé possèdent une région sans zéro à gauche de l'axe Rs=1 de la forme : [...]. À l'exception d'au plus d'une d'entre elles qui correspondrait alors à un caractère réel et qui aurait au plus un zéro réel dans cette zone. De plus, nous précisons que chaque fonction associée à un caractère donné possède au plus quatre zéros proches de l'axe réel dans la région [...]. Enfin, nous appliquons nos résultats à la répartition des nombres premiers dans une progression arithmétique de la forme {a+nq}
3 editions published between 2002 and 2013 in French and held by 3 WorldCat member libraries worldwide
Nous étudions la répartition des zéros non triviaux de la fonction Zêta de Riemann. Plus précisément, nous montrons qu'il n'y en a pas dans la région [...]. Les méthodes élaborées dans ce cas se généralisent alors à celui des fonctions de Dirichlet et nous établissons que les fonctions L associées à un module q fixé possèdent une région sans zéro à gauche de l'axe Rs=1 de la forme : [...]. À l'exception d'au plus d'une d'entre elles qui correspondrait alors à un caractère réel et qui aurait au plus un zéro réel dans cette zone. De plus, nous précisons que chaque fonction associée à un caractère donné possède au plus quatre zéros proches de l'axe réel dans la région [...]. Enfin, nous appliquons nos résultats à la répartition des nombres premiers dans une progression arithmétique de la forme {a+nq}
Monochromatic sums of squares by Gyan Prakash(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Sur un théorème de Mertens by
Olivier Ramaré(
)
1 edition published in 2002 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 2002 in German and held by 2 WorldCat member libraries worldwide
Contribution au probleme de Goldbach : tout entier superieur a 1 est somme d'au plus 13 nombres premiers by
Olivier Ramaré(
Book
)
2 editions published in 1991 in French and held by 2 WorldCat member libraries worldwide
Goldbach à conjecture en 1742 que tout entier supérieur à 1 est somme d'au plus 3 nombres premiers. On améliore le résultat de Riesel & Vaughan (1983) établissant que 19 nombres premiers suffisent, en montrant que 13 nombres premiers permettent de représenter tout entier supérieur à 1. La démonstration repose sur une majoration du nombre de représentations d'un entier en somme de trois nombres premiers; un des ingrédients est la détermination effective par Rumely de régions sans zéros pour les fonctSons L de Dirichlet associées à des caractères de petits conducteurs
2 editions published in 1991 in French and held by 2 WorldCat member libraries worldwide
Goldbach à conjecture en 1742 que tout entier supérieur à 1 est somme d'au plus 3 nombres premiers. On améliore le résultat de Riesel & Vaughan (1983) établissant que 19 nombres premiers suffisent, en montrant que 13 nombres premiers permettent de représenter tout entier supérieur à 1. La démonstration repose sur une majoration du nombre de représentations d'un entier en somme de trois nombres premiers; un des ingrédients est la détermination effective par Rumely de régions sans zéros pour les fonctSons L de Dirichlet associées à des caractères de petits conducteurs
Variations modernes sur la suite des nombres premiers : de la densité de la suite sin p lorsque p parcourt l'ensemble des
nombres premiers by
Olivier Ramaré(
Book
)
1 edition published in 2007 in French and held by 2 WorldCat member libraries worldwide
1 edition published in 2007 in French and held by 2 WorldCat member libraries worldwide
Quotient and product sets of thin subsets of the positive integers by
Javier Cilleruelo(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Séries de Dirichlet à deux variables et distribution des valeurs de fonctions arithmétiques by
Amandine Saldana(
Book
)
2 editions published in 2009 in French and held by 2 WorldCat member libraries worldwide
Nous traitons deux problèmes liés aux séries de Dirichlet. Nous étudions d'abord le prolongement analytique d'une certaine classe de séries de Dirichlet à deux variables: g(s_1,s_2,a,r) = somme_d≥1 r(d) / a(d)s1ds2, où a(d) est une fonction multiplicative strictement positive et r(d) est une fonction multiplicative. Nous démontrons, sous certaines hypothèses, un théorème général qui permet d'approcher cette série de Dirichlet par une série connue, modulo une autre série pour laquelle nous obtenons des majorations très précises. Nous utilisons ensuite cet outil pour obtenir des résultats quantitatifs sur la distribution des valeurs de fonctions arithmétiques. Sous certaines hypothèses sur les fonctions a(d) et r(d), nous déterminons lim_x→∞ 1/X somme_d<x_a(d)<z r(d) (0<z≤X) et mesurons la vitesse de convergence vers la loi limite. La classe de fonctions a(d) est beaucoup plus large que celle considérée jusqu'à maintenant. L'introduction de r(d) semble nouvelle
2 editions published in 2009 in French and held by 2 WorldCat member libraries worldwide
Nous traitons deux problèmes liés aux séries de Dirichlet. Nous étudions d'abord le prolongement analytique d'une certaine classe de séries de Dirichlet à deux variables: g(s_1,s_2,a,r) = somme_d≥1 r(d) / a(d)s1ds2, où a(d) est une fonction multiplicative strictement positive et r(d) est une fonction multiplicative. Nous démontrons, sous certaines hypothèses, un théorème général qui permet d'approcher cette série de Dirichlet par une série connue, modulo une autre série pour laquelle nous obtenons des majorations très précises. Nous utilisons ensuite cet outil pour obtenir des résultats quantitatifs sur la distribution des valeurs de fonctions arithmétiques. Sous certaines hypothèses sur les fonctions a(d) et r(d), nous déterminons lim_x→∞ 1/X somme_d<x_a(d)<z r(d) (0<z≤X) et mesurons la vitesse de convergence vers la loi limite. La classe de fonctions a(d) est beaucoup plus large que celle considérée jusqu'à maintenant. L'introduction de r(d) semble nouvelle
Discrepancy estimates for generalized polynomials by
Anirban Mukhopadhyay(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Intersection arithmétique et problème de Lehmer elliptique by
Bruno Winckler(
)
1 edition published in 2015 in French and held by 1 WorldCat member library worldwide
In this thesis we consider the problem of lower bounds for the canonical height onelliptic curves, aiming for the conjecture of Lehmer. Our main diophantine result isan explicit version of a theorem of Laurent (who proved this conjecture for ellipticcurves with CM up to a " exponent) using arithmetic intersection, enlightening thedependence with parameters linked to the elliptic curve ; such a result can be motivatedby the conjecture of Lang, hoping for a lower bound proportional to, roughly,the Faltings height of the curve.Nevertheless, our dissertation begins with a part dedicated to a completely explicitversion of the density theorem of Chebotarev, along the lines of a previous workdue to Lagarias and Odlyzko, which will be crucial to investigate the elliptic Lehmerproblem. We also obtain upper bounds for Siegel zeros, and for the smallest primeideal whose Frobenius is in a fixed conjugacy class
1 edition published in 2015 in French and held by 1 WorldCat member library worldwide
In this thesis we consider the problem of lower bounds for the canonical height onelliptic curves, aiming for the conjecture of Lehmer. Our main diophantine result isan explicit version of a theorem of Laurent (who proved this conjecture for ellipticcurves with CM up to a " exponent) using arithmetic intersection, enlightening thedependence with parameters linked to the elliptic curve ; such a result can be motivatedby the conjecture of Lang, hoping for a lower bound proportional to, roughly,the Faltings height of the curve.Nevertheless, our dissertation begins with a part dedicated to a completely explicitversion of the density theorem of Chebotarev, along the lines of a previous workdue to Lagarias and Odlyzko, which will be crucial to investigate the elliptic Lehmerproblem. We also obtain upper bounds for Siegel zeros, and for the smallest primeideal whose Frobenius is in a fixed conjugacy class
Quantitative steps in the Axer-Landau equivalence theorem by
Olivier Ramaré(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
Smoothing and cancellation : the Barban-Vehov sieve made explicit by
Sebastian Zuniga Alterman(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
From explicit estimates for primes to explicit estimates for the Möbius function by
Olivier Ramaré(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
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Related Identities
- Ramana, D. S. Other Collector Editor
- SpringerLink (Online service) Other
- Université Lille 1 - Sciences et technologies (Villeneuve-d'Ascq / 1970-2017) Degree grantor
- Rumely, Robert S.
- Queffélec, Hervé (19..-....). Thesis advisor
- École doctorale de mathématiques et informatique (Talence, Gironde) Other
- Institut de mathématiques de Bordeaux Other
- Kadiri, Habiba (1975-....). Author
- Deshouillers, Jean-Marc (1946-....). Other Thesis advisor
- Granville, Andrew Author
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Associated Subjects
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Alternative Names
Olivier Ramaré Frans wiskundige
Olivier Ramaré fransk matematikar
Olivier Ramaré fransk matematiker
Olivier Ramaré French mathematician
Olivier Ramaré matemàtic francès
Olivier Ramaré matemático francês
Olivier Ramaré matematico francese
Olivier Ramaré matemáticu francés
Olivier Ramare matematikan francez
Olivier Ramare matematisyen fransè
Ramaré, O.
Оливье Рамаре французский математик, специализирующийся на теории чисел и алгебре
オリヴィエ・ラマレ
奥利维尔·拉马尔
Languages