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

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

ISBN-10: 3319222392

ISBN-13: 9783319222394

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.

Show description

Read or Download Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday PDF

Best number theory books

The theory of numbers: an introduction

Help textual content for a primary path in quantity thought positive aspects using algebraic equipment for learning mathematics features. matters coated contain the Erdös-Selberg evidence of the leading quantity Theorem, an advent to algebraic and geometric quantity theory—the former through learning Gaussian and Jacobian integers, the latter via geometric equipment in proving the Quadratic Reciprocity legislations and in proofs of convinced asymptotic formulation for summatory services.

Mathematical Mysteries: The Beauty and Magic of Numbers

Why doubtless unrelated mathematical truths are hooked up in uncomplicated and lovely equations keeps to stump even mathematicians. This leisure math publication takes the reader on a lovely voyage into the area of common numbers. From the earliest discoveries of the traditional Greeks to numerous primary features of the normal quantity series, Clawson explains attention-grabbing mathematical mysteries in transparent and simple prose.

Elements of the Theory of Elliptic Functions

This ebook features a systematic presentation of the idea of elliptic services and a few of its purposes. A translation from the Russian, this e-book is meant essentially for engineers who paintings with elliptic features. it may be obtainable to these with historical past within the components of mathematical research and the idea of services contained in nearly the 1st years of arithmetic and physics classes on the university point.

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

Sample text

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.

Download PDF sample

Rated 4.77 of 5 – based on 46 votes