On the computation of coefficients of modular forms: the reduction modulo p approach

2012/11/06 by Jinxiang Zeng, Zeng, Jinxiang, Linsheng Yin +1
Mathematics · #11F30 #11F37 #11G20 #11Y16 #14H05 (Primary) #14Q05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F30 #msc:11F37 #msc:11G20 #msc:11Y16 #msc:14H05 #msc:14Q05

paper · pdf · doi:10.48550/arxiv.1211.1124

16 pages

arxiv created 2013/05/17 · arxiv updated 2013/05/20

Abstract

In this paper we present a probabilistic algorithm to compute the coefficients of modular forms of level one. Focus on the Ramanujan's tau function, we give out the explicit complexity of the algorithm. From a practical viewpoint, the algorithm is particularly well suited for implementations.

Related

• Computing Modular Polynomials
• The number of non-zero coefficients of modular forms (mod p)
• On the computation of Galois representations associated to level one modular forms
• A Computational Study of the Asymptotic Behaviour of Coefficient Fields of Modular Forms
• Note on the Tau Function