Equidistribution In Number Theory An Introduction
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Equidistribution In Number Theory An Introduction
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Author : Andrew Granville
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-08
Equidistribution In Number Theory An Introduction written by Andrew Granville and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-08 with Mathematics categories.
From July 11th to July 22nd, 2005, a NATO advanced study institute, as part of the series “Seminaire ́ de mathematiques ́ superieures”, ́ was held at the U- versite ́ de Montreal, ́ on the subject Equidistribution in the theory of numbers. There were about one hundred participants from sixteen countries around the world. This volume presents details of the lecture series that were given at the school. Across the broad panorama of topics that constitute modern number t- ory one nds shifts of attention and focus as more is understood and better questions are formulated. Over the last decade or so we have noticed incre- ing interest being paid to distribution problems, whether of rational points, of zeros of zeta functions, of eigenvalues, etc. Although these problems have been motivated from very di?erent perspectives, one nds that there is much in common, and presumably it is healthy to try to view such questions as part of a bigger subject. It is for this reason we decided to hold a school on “Equidistribution in number theory” to introduce junior researchers to these beautiful questions, and to determine whether di?erent approaches can in uence one another. There are far more good problems than we had time for in our schedule. We thus decided to focus on topics that are clearly inter-related or do not requirealotofbackgroundtounderstand.
An Introduction To Probabilistic Number Theory
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Author : Emmanuel Kowalski
language : en
Publisher: Cambridge University Press
Release Date : 2021-05-06
An Introduction To Probabilistic Number Theory written by Emmanuel Kowalski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.
A Pythagorean Introduction To Number Theory
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Author : Ramin Takloo-Bighash
language : en
Publisher: Springer
Release Date : 2018-11-26
A Pythagorean Introduction To Number Theory written by Ramin Takloo-Bighash and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-26 with Mathematics categories.
Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.
Introduction To Analytic And Probabilistic Number Theory
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Author : Gérald Tenenbaum
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-26
Introduction To Analytic And Probabilistic Number Theory written by Gérald Tenenbaum and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Mathematics categories.
This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. —Mathematical Reviews
Number Theory Fourier Analysis And Geometric Discrepancy
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Author : Giancarlo Travaglini
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-12
Number Theory Fourier Analysis And Geometric Discrepancy written by Giancarlo Travaglini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Mathematics categories.
Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.
Limit Theorems In Probability Statistics And Number Theory
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Author : Peter Eichelsbacher
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-23
Limit Theorems In Probability Statistics And Number Theory written by Peter Eichelsbacher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-23 with Mathematics categories.
Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.
Trends In Number Theory
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Author : Fernando Chamizo
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-28
Trends In Number Theory written by Fernando Chamizo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-28 with Mathematics categories.
This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain. The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).
Recent Developments In Operator Theory Mathematical Physics And Complex Analysis
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Author : Daniel Alpay
language : en
Publisher: Springer Nature
Release Date : 2023-04-11
Recent Developments In Operator Theory Mathematical Physics And Complex Analysis written by Daniel Alpay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-11 with Mathematics categories.
This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.
The Distribution Of Prime Numbers
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Author : Dimitris Koukoulopoulos
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-28
The Distribution Of Prime Numbers written by Dimitris Koukoulopoulos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-28 with Education categories.
Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources.
Analytic Methods In Arithmetic Geometry
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Author : Alina Bucur
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-22
Analytic Methods In Arithmetic Geometry written by Alina Bucur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-22 with Education categories.
In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with SL2(Fq) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from ℓ-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.