By Carl Pomerance, Michael Th. Rassias (eds.)
This quantity incorporates a choice of learn and survey papers written by means of probably 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 sphere. particular emphasis is given to issues 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 concerning the distribution of primes briefly durations, the Möbius functionality, Euler’s totient functionality, the Riemann zeta functionality and the Riemann speculation. Graduate scholars, examine mathematicians, in addition to computing device scientists and engineers who're drawn to natural and interdisciplinary examine, will locate this quantity an invaluable resource.
Contributors to this volume:
Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de l. a. 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 info for Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday
B. F. Swinnerton-Dyer, Notes on elliptic curves. I. J. Reine Angew. Math. 212, 7–25 (1963) 4. B. F. Swinnerton-Dyer, Notes on elliptic curves. II. J. Reine Angew. Math. 218, 79–108 (1965) 5. B. Conrey, L-Functions and random matrices, in Mathematics Unlimited: 2001 and Beyond (Springer, Berlin, 2001), pp. 331–352 6. B. Conrey, H. Iwaniec, Spacing of zeros of Hecke L-functions and the class number problem. Acta Arith. 103(3), 259–312 (2002) 7. H. Davenport, Multiplicative Number Theory (Graduate Texts in Mathematics), vol.
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.
We use the standard conventions. Specifically, by A B we mean jAj Ä cjBj for a positive constant c. Similarly, A B means A B and A B. 2 ix/, and define the Fourier transform of f by fO . x/e. N/ with N square-free. Thus u is an eigenfunction of the Laplacian with eigenvalue 1 1 itu /, and it is either even or odd with respect to the involution u DW . 2 C itu /. 2 z 7! 1=z; if u is even we set D 0, otherwise we take D 1. Selberg’s 3=16 ths theorem implies that we may take tu 0 or tu 2 Œ0; 14 i.