Lifting cusp forms to Maass forms with an application to partitions
نویسندگان
چکیده
منابع مشابه
Lifting 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...
متن کاملLifting Elliptic Cusp Forms to Maass Forms with an Application to Partitions
Abstract. For 2 < k ∈ 1 2 Z, we define lifts of cuspidal Poincaré series in Sk(Γ0(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 arising f...
متن کاملEffective 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 کاملLifting of Cusp forms from S̃L2 to GSpin(1, 4)
We construct liftings of cuspidal automorphic forms from the metaplectic group S̃L2 to GSpin(1, 4) using the Maaß Converse Theorem. In order to prove the non-vanishing of the lift we derive Waldspurger’s formula for Fourier coefficients of half integer weight Maaß forms. We analyze the automorphic representation of the adelic spin group obtained from the lift and show that it is CAP to the Saito...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2007
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.0611414104