Convolutions of Dirichlet series with the Fourier coefficients of cusp forms of weight 0

1982 ◽  
Vol 19 (2) ◽  
pp. 1194-1202
Author(s):  
N. V. Proskurin
Keyword(s):  
Dirichlet Series ◽  
Fourier Coefficients ◽  
Cusp Forms

Rankin–Cohen brackets on Jacobi forms of several variables and special values of certain Dirichlet series

2019 ◽  
Vol 15 (05) ◽  
pp. 925-933
Author(s):  
Abhash Kumar Jha ◽  
Brundaban Sahu
Keyword(s):  
Dirichlet Series ◽  
Scalar Product ◽  
Fourier Coefficients ◽  
Differential Operators ◽  
Cusp Forms ◽  
Jacobi Forms ◽  
Linear Map ◽  
Special Values ◽  
Several Variables

We construct certain Jacobi cusp forms of several variables by computing the adjoint of linear map constructed using Rankin–Cohen-type differential operators with respect to the Petersson scalar product. We express the Fourier coefficients of the Jacobi cusp forms constructed, in terms of special values of the shifted convolution of Dirichlet series of Rankin–Selberg type. This is a generalization of an earlier work of the authors on Jacobi forms to the case of Jacobi forms of several variables.

scholarly journals On the coefficients of symmetric power L-functions

2018 ◽  
Vol 14 (03) ◽  
pp. 813-824 ◽  
Author(s):  
Jaban Meher ◽  
Karam Deo Shankhadhar ◽  
G. K. Viswanadham
Keyword(s):  
Positive Integer ◽  
Dirichlet Series ◽  
Fourier Coefficient ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Prime Numbers ◽  
Cusp Forms ◽  
Symmetric Power ◽  
Fixed Positive Integer

We study the signs of the Fourier coefficients of a newform. Let [Formula: see text] be a normalized newform of weight [Formula: see text] for [Formula: see text]. Let [Formula: see text] be the [Formula: see text]th Fourier coefficient of [Formula: see text]. For any fixed positive integer [Formula: see text], we study the distribution of the signs of [Formula: see text], where [Formula: see text] runs over all prime numbers. We also find out the abscissas of absolute convergence of two Dirichlet series with coefficients involving the Fourier coefficients of cusp forms and the coefficients of symmetric power [Formula: see text]-functions.

scholarly journals On triple correlations of Fourier coefficients of cusp forms

2018 ◽  
Vol 183 ◽  
pp. 485-492 ◽  
Author(s):  
Guangshi Lü ◽  
Ping Xi
Keyword(s):  
Fourier Coefficients ◽  
Cusp Forms

scholarly journals On Dirichlet series attached to cusp forms and the Siegel-zero

1984 ◽  
Vol 25 (1) ◽  
pp. 107-119 ◽  
Author(s):  
F. Grupp
Keyword(s):  
Dirichlet Series ◽  
Cusp Form ◽  
Fourier Expansion ◽  
Dirichlet Character ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Siegel Zero ◽  
Image Position

Let k be an even integer greater than or equal to 12 and f an nonzero cusp form of weight k on SL(2, Z). We assume, further, that f is an eigenfunction for all Hecke-Operators and has the Fourier expansionFor every Dirichlet character xmod Q we define

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