On the zeros of linear combinations of the matsumoto zeta-functions

1998 ◽  
Vol 38 (2) ◽  
pp. 144-159 ◽  
Author(s):  
A. Laurinčikas
Keyword(s):  
Zeta Functions ◽  
Linear Combinations

scholarly journals MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS

2017 ◽  
Vol 232 ◽  
pp. 19-54 ◽  
Author(s):  
MASANOBU KANEKO ◽  
HIROFUMI TSUMURA
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Bernoulli Numbers ◽  
Multiple Zeta Values ◽  
Linear Combinations ◽  
Multiple Zeta ◽  
Zeta Values ◽  
The One ◽  
Positive Integers

We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as the one to be paired up with the $\unicode[STIX]{x1D709}$-function defined by Arakawa and Kaneko. We show that both are closely related to the multiple zeta functions. Further we define multi-indexed poly-Bernoulli numbers, and generalize the duality formulas for poly-Bernoulli numbers by introducing more general zeta functions.

Joint discrete universality for periodic zeta-functions. II

2019 ◽  
Vol 43 (12) ◽  
pp. 1765-1779 ◽  
Author(s):  
Antanas Laurinčikas
Keyword(s):  
Zeta Functions ◽  
Discrete Universality
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