Haberland’s formula and numerical computation of Petersson scalar products
نویسندگان
چکیده
منابع مشابه
Haberland’s Formula and Numerical Computation of Petersson Scalar Products
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 Γ = PSL2(Z), which gives a fast method to compute these scalar products when a Hecke eigenbasis is not necessarily available.
متن کاملNUMERICAL COMPUTATION OF PETERSSON INNER PRODUCTS AND q-EXPANSIONS
In this paper we discuss the problem of numerically computing Petersson inner products of modular forms, given their q-expansion at∞. A formula of Nelson [Nel15] reduces this to obtaining q-expansions at all cusps, and we describe two algorithms based on linear interpolation for numerically obtaining such expansions. We apply our methods to numerically verify constants arising in an explicit ve...
متن کاملNUMERICAL COMPUTATION OF PETERSSON INNER PRODUCTS AND q-EXPANSIONS - PRELIMINARY VERSION
In this paper we discuss the problem of numerically computing Petersson inner products of modular forms, given their q-expansion at∞. A formula of Nelson [Nel15] reduces this to obtaining q-expansions at all cusps, and we describe two algorithms based on linear interpolation for numerically obtaining such expansions. We apply our methods to numerically verify constants arising in an explicit ve...
متن کاملOn the transcendence of certain Petersson inner products
We show that for all normalized Hecke eigenforms $f$ with weight one and of CM type, the number $(f,f)$ where $(cdot, cdot )$ denotes the Petersson inner product, is a linear form in logarithms and hence transcendental.
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ژورنال
عنوان ژورنال: The Open Book Series
سال: 2013
ISSN: 2329-907X,2329-9061
DOI: 10.2140/obs.2013.1.249