Generating functions for Hecke operators
Number Theory
2012-04-09 v1
Abstract
Fix a prime N, and consider the action of the Hecke operator T_N on the space M_k(SL(2,Z)) of modular forms of full level and varying weight k. The coefficients of the matrix of T_N with respect to the basis {E_4^i E_6^j | 4i + 6j = k} for M_k(SL(2,Z)) can be combined for varying k into a generating function F_N. We show that this generating function is a rational function for all N, and present a systematic method for computing F_N. We carry out the computations for N = 2, 3, 5, and indicate and discuss generalizations to spaces of modular forms of arbitrary level.
Keywords
Cite
@article{arxiv.math/0610962,
title = {Generating functions for Hecke operators},
author = {Hala Hajj Shehadeh and Samar Jaafar and Kamal Khuri-Makdisi},
journal= {arXiv preprint arXiv:math/0610962},
year = {2012}
}
Comments
13 pages