Analytic number theory : in honor of Helmut Maier's 60th birthday
著者
書誌事項
Analytic number theory : in honor of Helmut Maier's 60th birthday
Springer, c2015
- : pbk
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注記
Includes bibliographical references
内容説明・目次
内容説明
This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Moebius function, Euler's totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource.
Contributors to this volume:
Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Regis de la Breteche, 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 Ivic, 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, Janos Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwill, Joel Rivat, Andras Sarkoezy, Jeffrey Shallit, Terence Tao, Gerald Tenenbaum, Laszlo Toth, Tamar Ziegler, Liyang Zhang.
目次
CM-Points on Straight Lines.- Maass Waveforms and Low-Lying Zeros.- Theoreme de Jordan Friable.- On Conjectures of T. Ordowski and Z.W. Sun Concerning Primes and Quadratic Forms.- Large Gaps Between Consecutive Prime Numbers Containing Perfect Powers.- On the Parity of the Number of Small Divisors of n.- Counting Primes in Arithmetic Progressions.- Limit Points of the Sequence of Normalized Differences Between Consecutive Prime Numbers.- Spirals of the Zeta Function I.- Best Possible Densities of Dickson m-tuples, as a Consequence of Zhang-Maynard-Tao.- A Note on Helson's Conjecture on Moments of Random Multiplicative Functions.- Large Values of the Zeta-Function on the Critical Line.- A Note on Bessel Twists of L-Functions.- The Sound of Fractal Strings and the Riemann Hypothesis.- Sums of two Squares in Short Intervals.- Infinite Sumsets with Many Representations.- On the Ratio of Consecutive Gaps Between Primes.- Remarks on Fibers of the Sum-of-Divisors Function.- On Amicable Numbers.- Trigonometric Representations of Generalized Dedekind and Hardy Sums via the Discrete Fourier Transform.- On Arithmetic Properties of Products and Shifted Products.- Narrow Progressions in the Primes.
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