Irregularities in the Distribution of Prime Numbers [electronic resource] : From the Era of Helmut Maier's Matrix Method and Beyond / edited by János Pintz, Michael Th. Rassias
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- 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).
- 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.
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