Fourier coefficients of nonholomorphic modular forms and sums of Kloosterman sums
نویسندگان
چکیده
منابع مشابه
On Sums of Fourier Coefficients of Cusp Forms
in case f(n) is the Fourier coefficient of a holomorphic or non-holomorphic cusp form. We shall first deal with the latter case, which is more complicated. Let as usual {λj = κj + 14} ∪ {0} be the discrete spectrum of the non-Euclidean Laplacian acting on SL(2,Z) –automorphic forms. Further let ρj(n) denote the n-th Fourier coefficient of the Maass wave form φj(z) corresponding to the eigenvalu...
متن کاملLegendre Sums, Soto-andrade Sums and Kloosterman Sums
The three sums named in the title are all known to appear in connection with the complex representation theory of GL(2, q). The first two are incarnations of certain spherical vectors, whereas the third is a matrix coefficient for a parabolic basis. In this work, Legendre and Soto-Andrade sums are shown to occur in a second way, as parabolic ClebschGordan coefficients for the tensor product of ...
متن کاملFourier Coefficients of Modular Forms
These notes describe some conjectures and results related to the distribution of Fourier coefficients of modular forms. This is a rough draft and these notes should forever be considered incomplete.
متن کاملOn the Fourier coefficients of nonholomorphic Hilbert modular forms of half-integral weight
Let f(z) = ∑ n≥1 ane 2πinz be a Hecke eigenform of half-integral weightm+1/2, and let g(z) = ∑ n≥1 bne 2πinz be the corresponding even-weight form, in the sense of [Sh 73]. In particular, g has weight 2m, and belongs to the same eigenvalues of Hecke operators as f . If n = qr with squarefree r, then an is expressible in terms of ar and the {bj}. At the end of [Sh 77], Shimura suggested that ar ...
متن کاملModular Invariants for Real Quadratic Fields and Kloosterman Sums
We investigate the asymptotic distribution of integrals of the j-function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asymptotic formula, we prove a bound for sums of Kloosterman sums of half-integral weight which is uniform in every parameter. To establish this estimate we prove a variant of Kuznetsov’s formula where the spectral data is re...
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: Pacific Journal of Mathematics
سال: 1991
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1991.148.303