On special values of Dirichlet series with periodic coefficients

2021 ◽  
Author(s):  
Abhishek Bharadwaj ◽  
Siddhi Pathak
Keyword(s):  
Dirichlet Series ◽  
Periodic Coefficients ◽  
Special Values

scholarly journals Approximation by special values of Dirichlet series

2019 ◽  
Vol 148 (1) ◽  
pp. 83-93
Author(s):  
Şermin Çam Çelik ◽  
Haydar Göral
Keyword(s):  
Dirichlet Series ◽  
Special Values

Dirichlet series with periodic coefficients

1999 ◽  
Vol 35 (1-2) ◽  
pp. 70-88 ◽  
Author(s):  
Makoto Ishibashi ◽  
Shigeru Kanemitsu
Keyword(s):  
Dirichlet Series ◽  
Periodic Coefficients

scholarly journals SPECIAL VALUES OF DIRICHLET SERIES AND ZETA INTEGRALS

2012 ◽  
Vol 08 (03) ◽  
pp. 697-714 ◽  
Author(s):  
EDUARDO FRIEDMAN ◽  
ALDO PEREIRA
Keyword(s):  
Positive Integer ◽  
Analytic Continuation ◽  
Dirichlet Series ◽  
Direct Calculation ◽  
Simple Relation ◽  
Product Rule ◽  
Special Values ◽  
Special Value

For f and g polynomials in p variables, we relate the special value at a non-positive integer s = -N, obtained by analytic continuation of the Dirichlet series [Formula: see text], to special values of zeta integrals Z(s;f,g) = ∫x∊[0, ∞)p g(x)f(x)-s dx ( Re (s) ≫ 0). We prove a simple relation between ζ(-N;f,g) and Z(-N;fa, ga), where for a ∈ ℂp, fa(x) is the shifted polynomial fa(x) = f(a + x). By direct calculation we prove the product rule for zeta integrals at s = 0, degree (fh) ⋅ Z(0;fh, g) = degree (f) ⋅ Z(0;f, g) + degree (h) ⋅ Z(0;h, g), and deduce the corresponding rule for Dirichlet series at s = 0, degree (fh) ⋅ ζ(0;fh, g) = degree (f) ⋅ ζ(0;f, g)+ degree (h)⋅ζ(0;h, g). This last formula generalizes work of Shintani and Chen–Eie.

scholarly journals SPECIAL VALUES OF SHIFTED CONVOLUTION DIRICHLET SERIES

Mathematika ◽  
2015 ◽  
Vol 62 (1) ◽  
pp. 47-66 ◽  
Author(s):  
Michael H. Mertens ◽  
Ken Ono
Keyword(s):  
Dirichlet Series ◽  
Special Values

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.

Sign in / Sign up

Export Citation Format

Share Document