Olivier Ramaré – författare

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5 produkter

Excursions in Multiplicative Number Theory
AvOlivier Ramaré
Inbunden, Engelska, 2022
831 kr
Skickas inom 10-15 vardagar
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 asthe Selberg formula, Brun’s sieve, 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.
Excursions in Multiplicative Number Theory
AvOlivier Ramare
E-bok
Engelska, 2022
797 kr
Läs direkt efter köp
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 asthe Selberg formula, Brun’s sieve, 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.
Excursions in Multiplicative Number Theory
AvOlivier Ramaré
Häftad, Engelska, 2023
334 kr
Skickas inom 5-8 vardagar
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 asthe Selberg formula, Brun’s sieve, 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
AvOlivier Ramare,D.S. Ramanam. fl.
Häftad, Engelska, 2009
480 kr
Skickas inom 5-8 vardagar
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.
Arithmetical Aspects of the Large Sieve Inequality
AvD. S. Ramana,Olivier Ramaré
Inbunden, Engelska, 2027
1 743 kr
Kommande
This book develops a unified, modern framework for the large sieve and the Selberg sieve, built on a common system of Hermitian inequalities. It connects classical arguments with more recent methods and applications in analytic and algebraic number theory. The exposition includes improved Brun–Titchmarsh-type bounds, large sieve extensions for sifted sequences, and a development of the enveloping sieve arising from the Selberg sieve. An appendix gathers the relevant mean-value estimates and technical tools into a coherent reference.Several parts are written with particular audiences in mind. In particular, the chapters on enveloping sieves for the squares and on prime powers and number fields, are aimed, respectively, at harmonic analysts and algebraic number theorists. This second edition refreshes and extends the bibliography and updates the 2005 lecture notes in three main directions. It adds new theoretical material, including Nazarov’s extremal examples, a new Hilbertian basis, Huxley’s lower bound, and explicit smoothings of Holt and Vaaler. Moreover, it expands applications of the Brun–Titchmarsh inequality to products of three primes, an oscillatory sum, and norms in number fields, and it develops further the Selberg sieve as an enveloping sieve, incorporating ideas in the spirit of Green–Tao. This monograph is aimed at researchers and advanced graduate students, offering a unified perspective on classical methods and modern developments in mathematical research.

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Olivier Ramaré – författare

Excursions in Multiplicative Number Theory

Excursions in Multiplicative Number Theory

Excursions in Multiplicative Number Theory

Arithmetical Aspects of the Large Sieve Inequality

Arithmetical Aspects of the Large Sieve Inequality

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