Irregularities in the Distribution of Prime Numbers

1. Front Matter

   Pages i-xi

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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

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.

• analytic number theory
• approximation theory
• probabilistic theory
• additive number theory
• computational number theory
• Vinogradov's mean value theorem
• Euler totient function
• Euler-Kronecker constants

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

  János Pintz

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

  Michael Th. Rassias

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. 

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