Functiones et Approximatio Commentarii Mathematici

Rankin-Cohen Brackets on Hilbert Modular forms and Special values of certain Dirichlet series

Moni Kumari and Brundaban Sahu

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Abstract

Given a fixed Hilbert modular form, we consider a family of linear maps between the spaces of Hilbert cusp forms by using the Rankin-Cohen brackets and then we compute the adjoint maps of these linear maps with respect to the Petersson scalar product. The Fourier coefficients of the Hilbert cusp forms constructed using this method involve special values of certain Dirichlet series of Rankin-Selberg type associated to Hilbert cusp forms.

Article information

Source
Funct. Approx. Comment. Math., Volume 58, Number 2 (2018), 257-268.

Dates
First available in Project Euclid: 2 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1512183766

Digital Object Identifier
doi:10.7169/facm/1703

Mathematical Reviews number (MathSciNet)
MR3816079

Zentralblatt MATH identifier
06924932

Subjects
Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Secondary: 11F60: Hecke-Petersson operators, differential operators (several variables) 11F68: Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series

Keywords
Hilbert modular forms Rankin-Cohen brackets Dirichlet series adjoint map

Citation

Kumari, Moni; Sahu, Brundaban. Rankin-Cohen Brackets on Hilbert Modular forms and Special values of certain Dirichlet series. Funct. Approx. Comment. Math. 58 (2018), no. 2, 257--268. doi:10.7169/facm/1703. https://projecteuclid.org/euclid.facm/1512183766


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