# Get Analytic Number Theory: In Honor of Helmut Maier's 60th PDF

By Carl Pomerance, Michael Th. Rassias (eds.)

ISBN-10: 3319222392

ISBN-13: 9783319222394

This quantity encompasses a number of examine and survey papers written via the most eminent mathematicians within the overseas group and is devoted to Helmut Maier, whose personal examine has been groundbreaking and deeply influential to the sector. particular emphasis is given to themes concerning exponential and trigonometric sums and their habit in brief durations, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted leading numbers, oscillation theorems for primes in mathematics progressions, inequalities on the topic of the distribution of primes in brief periods, the Möbius functionality, Euler’s totient functionality, the Riemann zeta functionality and the Riemann speculation. Graduate scholars, learn mathematicians, in addition to laptop scientists and engineers who're drawn to natural and interdisciplinary study, will locate this quantity an invaluable resource.

*Contributors to this volume:*

Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de los angeles Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.

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**Extra resources for Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday**

**Sample text**

Proof. uj /: (116) As before, we apply the Kuznetsov formula to the inner sum. Since the formula has a ıp1 ;p2 , we need to split this sum into the case when p1 D p2 and the case when p1 ¤ p2 . For small support one easily finds the case p1 ¤ p2 does not contribute; however, the case p1 D p2 does contribute. z/dz C O log R 1 1 (117) (the equality follows from partial summation and the Prime Number Theorem, see [42] for a proof). 3. 2; 2/. uj ; 2/ terms Proof. The proof is similar to the previous lemma, following again by applications of the Kuznetsov trace formula.

2009). 1112/plms/pdp018 10. M. Edwards, Riemann’s Zeta Function (Academic, New York, 1974) 11. A. Entin, E. Roditty-Gershon, Z. Rudnick, Low-lying zeros of quadratic Dirichlet L-functions, hyper-elliptic curves and random matrix theory. Geom. Funct. Anal. 23(4), 1230–1261 (2013) 12. P. Erd˝os, H. Maier, A. Sárközy, On the distribution of the number of prime factors of sums a C b. Trans. Am. Math. Soc. 302(1), 269–280 (1987) 13. D. J. Miller, Surpassing the ratios conjecture in the 1-level density of Dirichlet L-functions.

Liu, Y. Ye, Petersson and Kuznetsov trace formulas, in Lie Groups and Automorphic Forms, ed. by L. -S. W. -T. Yau, AMS/IP Studies in Advanced Mathematics, vol. 37 (American Mathematical Society, Providence, 2006), pp. 147–168 36. H. Maier, On Exponential Sums with Multiplicative Coefficients, in Analytic Number Theory (Cambridge University Press, Cambridge 2009), pp. 315–323 37. H. Maier, C. Pomerance, Unusually large gaps between consecutive primes. Trans. Am. Math. Soc. 322(1), 201–237 (1990) 38.

### Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday by Carl Pomerance, Michael Th. Rassias (eds.)

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