Irregularities in the Distribution of Prime Numbers (eBook)

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

János Pintz, Michael Th. Rassias (Herausgeber)

eBook Download: PDF

2018 | 1st ed. 2018
XI, 217 Seiten
Springer International Publishing (Verlag)
978-3-319-92777-0 (ISBN)

Infos

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.

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. 

Inhalt

Foreword (H. Maier).- Preface.- 1. Chains of Large Gaps Between Primes (K. Ford, J. Maynard, T. Tao).- 2. A Note on the Distrution of Primes in Intervals (T. Freiberg).- 3. Distribution of Large Gaps Between Primes (S. Funkhouser, D.A. Goldston, A.H. Ledoan).- 4. On the Difference in Values of the Euler Totient Function Near Prime Arguments (S.R. Garcia, F. Luca).- 5. Vinogradov's Mean Value Theorem As an Ingredient in Polynomial Large Sieve Inequalities and Some Consequences (K. Halupczok).- 6. Unexpected Regularities in the Behavior of Some Number-Theoretic Power Series (A.J. Hildebrand).- 7. The Convex Hull of the Prime Number Graph (N. McNew).- 8. Irregular Behaviour of Class Numbers and Euler-Kronecker Constants of Cyclotomic Fields: the Log Log Log Devil at Play (P. Moree).- 9. Maier's Matrix Method and Irregularities in the Distribution of Prime Numbers (A. Raigorodskii, M.Th. Rassias).- 10. Sums of Values of Non-Principal Characters Over Shifted Primes (R.Z. Khusenovich).

Produkt-Details

• Erscheint lt. Verlag: 4.7.2018
• Zusatzinfo: XI, 217 p. 13 illus., 1 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: additive number theory • Analytic number theory • Approximation Theory • Computational Number Theory • Euler-Kronecker constants • Euler Totient Function • probabilistic theory • Vinogradov's mean value theorem
• ISBN-10: 3-319-92777-9 / 3319927779
• ISBN-13: 978-3-319-92777-0 / 9783319927770