منابع مشابه
Effective Computation of Maass Cusp Forms
We study theoretical and practical aspects of high-precision computation of Maass forms. First, we compute to over 1000 decimal places the Laplacian and Hecke eigenvalues for the first few Maass forms on PSL(2,Z)\H. Second,we give an algorithm for rigorously verifying that a proposed eigenvalue together with a proposed set of Fourier coefficients indeed correspond to a true Maass cusp form. We ...
متن کاملMaass Cusp Forms for Large Eigenvalues
We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.
متن کاملA Large Sieve Zero Density Estimate for Maass Cusp Forms
A Large Sieve Zero Density Estimate for Maass Cusp Forms Paul Dunbar Lewis The large sieve method has been used extensively, beginning with Bombieri in 1965, to provide bounds on the number of zeros of Dirichlet L-functions near the line σ = 1. Using the Kuznetsov trace formula and the work of Deshouillers and Iwaniec on Kloosterman sums, it is possible to derive large sieve inequalities for th...
متن کاملSpecial Values of Koecher-maass Series of Siegel Cusp Forms
The purpose of this paper is to give a generalization of the above result to the case of a Siegel cusp form f , where now L(f, χ, s) is replaced by an appropriate χ-twist of the Koecher-Maass series attached to f . More precisely, let f be a cusp form of even integral weight k ≥ g + 1 w.r.t. the Siegel modular group Γg := Spg(Z) of genus g and write a(T ) (T a positive definite half-integral ma...
متن کاملLifting cusp forms to Maass forms with an application to partitions.
For 2 < k [abstract: see text] we define lifts of cuspidal Poincaré series in S(k)(Gamma(0)(N)) to weight 2 - k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework "explaining" Ramanujan's mock theta functions. As an application, we show that the number of partitions of a positive integer n is the "trace" of singular moduli of a Maass form...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1985
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.82.11.3533