منابع مشابه
Sign Changes of Hecke Eigenvalues
in the Maass case. In [14] Kowalski, Lau, Soundararajan and Wu investigate the problem of the first sign change of λf (n) for holomorphic f . They remark on the similarities with the problem of the least quadratic residue. This motivates the point of view that the signs of λf (n) are GL(2) analogues of real characters. The frequency of signs and sign changes and other related questions have bee...
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Introduction In one form or another, data transforms underpin a large part of contemporary signal processing, whether in geophysics, communications, or video and image processing. I begin this overview by describing why transforms are of interest, and how we can conceive of a transform. I use three well known, but distinct, classes of transform, namely the Fourier, Radon, and eigenvector transf...
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Article history: Received 13 October 2007 Revised 9 May 2008 Available online 17 December 2008 Communicated by David Goss In 1997, Serre proved an equidistribution theorem for eigenvalues of Hecke operators on the space S(N,k) of cusp forms of weight k and level N . In this paper, we derive an effective version of Serre’s theorem. As a consequence, we estimate, for a given d and prime p coprime...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2007
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x07002679