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

Chowla’s theorem over function fields

2018 ◽  
Vol 14 (06) ◽  
pp. 1689-1698
Author(s):  
Yoshinori Hamahata
Keyword(s):  
Dirichlet Series ◽  
Function Field ◽  
Function Fields ◽  
Rational Numbers ◽  
Periodic Coefficients ◽  
Linearly Independent ◽  
Parity Condition

Sarvadaman Chowla proved that if [Formula: see text] is an odd prime, then [Formula: see text] ([Formula: see text]) are linearly independent over the field of rational numbers. We establish an analog of this result over function fields. As an application, we prove an analog of the Baker–Birch–Wirsing theorem about the non-vanishing of Dirichlet series with periodic coefficients at [Formula: see text] in the function field setup with a parity condition.

scholarly journals Non-vanishing of Dirichlet series with periodic coefficients

2014 ◽  
Vol 145 ◽  
pp. 1-21 ◽  
Author(s):  
Tapas Chatterjee ◽  
M. Ram Murty
Keyword(s):  
Dirichlet Series ◽  
Periodic Coefficients

scholarly journals Joint universality of periodic zeta-functions with multiplicative coefficients

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Antanas Laurinčikas ◽  
Monika Tekorė
Keyword(s):  
Zeta Function ◽  
Dirichlet Series ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Periodic Coefficients ◽  
Joint Universality

The periodic zeta-function is defined by the ordinary Dirichlet series with periodic coefficients. In the paper, joint universality theorems on the approximation of a collection of analytic functions by nonlinear shifts of periodic zeta-functions with multiplicative coefficients are obtained. These theorems do not use any independence hypotheses on the coefficients of zeta-functions.

scholarly journals A WEIGHTED UNIVERSALITY THEOREM FOR PERIODIC ZETA-FUNCTIONS

2017 ◽  
Vol 22 (1) ◽  
pp. 95-105 ◽  
Author(s):  
Renata Macaitienė ◽  
Mindaugas Stoncelis ◽  
Darius Šiaučiūnas
Keyword(s):  
Zeta Function ◽  
Dirichlet Series ◽  
Complex Plane ◽  
Wide Class ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Periodic Coefficients ◽  
Universality Theorem

The periodic zeta-function ζ(s; a), s = σ + it is defined for σ > 1 by the Dirichlet series with periodic coefficients and is meromorphically continued to the whole complex plane. It is known that the function ζ(s; a), for some sequences a of coefficients, is universal in the sense that its shifts ζ(s + iτ ; a), τ ∈ R, approximate a wide class of analytic functions. In the paper, a weighted universality theorem for the function ζ(s; a) is obtained.

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