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

ISBN-10: 3319222392

ISBN-13: 9783319222394

This quantity incorporates a selection of learn and survey papers written through essentially the most eminent mathematicians within the foreign neighborhood and is devoted to Helmut Maier, whose personal study has been groundbreaking and deeply influential to the sector. particular emphasis is given to issues relating to exponential and trigonometric sums and their habit briefly periods, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted major numbers, oscillation theorems for primes in mathematics progressions, inequalities regarding the distribution of primes briefly periods, the Möbius functionality, Euler’s totient functionality, the Riemann zeta functionality and the Riemann speculation. Graduate scholars, examine mathematicians, in addition to machine scientists and engineers who're drawn to natural and interdisciplinary learn, 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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**Additional resources for Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday**

**Example text**

Compos. Math. 140, 952–992 (2004) 44. J. Miller, D. Montague, An orthogonal test of the L-functions ratios conjecture, II. Acta Arith. 146, 53–90 (2011) 45. J. Miller, R. Peckner, Low-lying zeros of number field L-functions. J. Number Theory 132, 2866–2891 (2012) 46. J. Miller, R. Takloo-Bighash, An Invitation to Modern Number Theory (Princeton University Press, Princeton, 2006) 47. H.

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. 74, 2nd edn. (Springer, New York, 1980). Revised by H. Montgomery 8. E. J. 6/ family of L-functions. Compos. Math. 142(6), 1403–1425 (2006) 9.

1; 1/, or compute the 2level density, as that is different for the three orthogonal groups for arbitrarily small support [42, 43]. The Katz–Sarnak Density Conjecture states that the behavior of zeros near the central point in a family of L-functions (as the conductors tend to infinity) agrees with the behavior of eigenvalues near 1 of a classical compact group (as the matrix size tends to infinity). 6/ L-functions; see, for example, [8, 9, 11, 13, 16, 17, 20, 23, 24, 27, 29, 32, 43, 45, 50, 51, 53, 54, 59, 60].

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