Cusp Forms Whose Fourier Coefficients Involve Dirichlet Series
Uğur S. Kırmacı *
Department of Mathematics, K. K. Education Faculty, Atatürk University, Erzurum, 25240, Turkey.
*Author to whom correspondence should be addressed.
Abstract
We present some cusp forms on the full modular group ⌈1, using the properties of eigenfunctions, nonanalytic Poincare series and Hecke operators Tn. Further, the Fourier coefficients of cusp forms Tnf on ⌈1 are given in terms of Dirichlet series associated to the Fourier coefficients of cusp form f of weight k.
Keywords: Cusp forms, eigenfunctions, nonanalytic Poincare series, Dirichlet series, Hecke operators.