Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms write by Andrew Knightly. This book was released on 2013. Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms available in PDF, EPUB and Kindle.
Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms
Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms write by Andrew Knightly. This book was released on 2013-06-28. Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms available in PDF, EPUB and Kindle. The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.
Analytic Number Theory
Analytic Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic Number Theory write by Carl Pomerance. This book was released on 2015-11-18. Analytic Number Theory available in PDF, EPUB and Kindle. 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 Möbius 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, Régis de la 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.
An Introduction to Automorphic Representations
An Introduction to Automorphic Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Automorphic Representations write by Jayce R. Getz. This book was released on . An Introduction to Automorphic Representations available in PDF, EPUB and Kindle.
The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates
The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates write by Robert J. Buckingham. This book was released on 2013-08-23. The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates available in PDF, EPUB and Kindle. The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.
