Haberland's formula and numerical computation of Petersson scalar products

Henri Cohen (1, 2)

1 LFANT - Lithe and fast algorithmic number theory
2 IMB - Institut de Mathématiques de Bordeaux

We study several methods for the numerical computation of Petersson scalar products, and in particular we prove a generalization of Haberland's formula to any subgroup of finite index G of Gamma = PSL_2 (Z), which gives a fast method to compute these scalar products when a Hecke eigenbasis is not necessarily available.

Domaines: Théorie des nombres [math.NT]

Henri Cohen. Haberland's formula and numerical computation of Petersson scalar products. ANTS X, 2012, San Diego, United States. pp.249-270, ⟨10.2140/obs.2013.1.249⟩. ⟨hal-00854440⟩