Petersson inner products of weight-one modular forms
نویسندگان
چکیده
منابع مشابه
On Dirichlet Series and Petersson Products for Siegel Modular Forms
— We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree n and weight k > n/2 has meromorphic continuation to C. Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight k > n/2 may be expressed in terms of the residue at s = k of the associated Dirichlet series....
متن کاملModular Forms of Weight One
The decomposition into an Euler product and the functional equation of the Dirichlet series associated by Hecke to modular forms of weight one suggests that these correspond to Artin L-functions of degree 2 over Q, otherwise known as Galois representations Gal(Q/Q)→ GL2(C). It is this correspondence, conjectured by Langlands, which we establish here. The first three sections are preliminary. Th...
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.
متن کاملMock-modular Forms of Weight One
The object of this paper is to initiate a study of the Fourier coefficients of a weight one mock-modular form and relate them to the complex Galois representations associated to the form’s shadow, which is a weight one newform. In this paper, our focus will be on weight one dihedral newforms of prime level p ≡ 3 (mod 4). In this case we give properties of the Fourier coefficients themselves tha...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2019
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2016-0042