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Irregularities in the Distribution of Prime Numbers

From the Era of Helmut Maier's Matrix Method and Beyond

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  • © 2018

Overview

Editors:
  1. János Pintz

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

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  2. Michael Th. Rassias

    1. Institute of Mathematics, University of Zürich, Zürich, Switzerland

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  • Contains open problems and new directions for future research in a simple, self-contained format

  • Features contributions by experts from the international community

  • Provides an historical overview of a large body of research in analytic number theory and approximation theory

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Chains of Large Gaps Between Primes

    • Kevin Ford, James Maynard, Terence Tao
    Pages 1-21

  3. A Note on the Distribution of Primes in Intervals

    • Tristan Freiberg
    Pages 23-44

  4. Distribution of Large Gaps Between Primes

    • Scott Funkhouser, Daniel A. Goldston, Andrew H. Ledoan
    Pages 45-67

  5. On the Difference in Values of the Euler Totient Function Near Prime Arguments

    • Stephan Ramon Garcia, Florian Luca
    Pages 69-96

  6. Vinogradov’s Mean Value Theorem as an Ingredient in Polynomial Large Sieve Inequalities and Some Consequences

    • Karin Halupczok
    Pages 97-109

  7. Unexpected Regularities in the Behavior of Some Number-Theoretic Power Series

    • A. J. Hildebrand
    Pages 111-123

  8. The Convex Hull of the Prime Number Graph

    • Nathan McNew
    Pages 125-141

  9. Irregular Behaviour of Class Numbers and Euler-Kronecker Constants of Cyclotomic Fields: The Log Log Log Devil at Play

    • Pieter Moree
    Pages 143-163

  10. Maier’s Matrix Method and Irregularities in the Distribution of Prime Numbers

    • Andrei Raigorodskii, Michael Th. Rassias
    Pages 165-186

  11. Sums of Values of Nonprincipal Characters over Shifted Primes

    • Zarullo Rakhmonov
    Pages 187-217
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Keywords

About this book

This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.


Editors and Affiliations

  • Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    János Pintz

  • Institute of Mathematics, University of Zürich, Zürich, Switzerland

    Michael Th. Rassias

About the editors

János Pintz is a Hungarian mathematician working in analytic number theory. He is a fellow of the Rényi Mathematical Institute and is also a member of the Hungarian Academy of Sciences. In 2014, he received the Cole Prize.


Michael Th. Rassias is a Latsis Foundation Senior Fellow at the University of Zürich and a visiting researcher at the Institute for Advanced Study, Princeton. He has also been a researcher at ETH-Zürich and Princeton University. While at Princeton, he collaborated with John F. Nash, Jr., for the Springer volume Open Problems in Mathematics. 

Bibliographic Information

  • Book Title: Irregularities in the Distribution of Prime Numbers

  • Book Subtitle: From the Era of Helmut Maier's Matrix Method and Beyond

  • Editors: János Pintz, Michael Th. Rassias

  • DOI: https://doi.org/10.1007/978-3-319-92777-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-92776-3Published: 16 July 2018

  • Softcover ISBN: 978-3-030-06514-0Published: 08 February 2019

  • eBook ISBN: 978-3-319-92777-0Published: 04 July 2018

  • Edition Number: 1

  • Number of Pages: XI, 217

  • Number of Illustrations: 12 b/w illustrations, 1 illustrations in colour

  • Topics: Number Theory, Functions of a Complex Variable, Special Functions

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