scholarly journals Multiple zeta functions: the double sine function and the signed double Poisson summation formula

2004 ◽  
Vol 140 (05) ◽  
pp. 1176-1190 ◽  
Author(s):  
Shin-ya Koyama ◽  
Nobushige Kurokawa
Keyword(s):  
Zeta Functions ◽  
Summation Formula ◽  
Poisson Summation Formula ◽  
Sine Function ◽  
Multiple Zeta ◽  
Double Sine Function ◽  
Poisson Summation

scholarly journals EULER PRODUCT EXPRESSION OF TRIPLE ZETA FUNCTIONS

2005 ◽  
Vol 16 (02) ◽  
pp. 111-136
Author(s):  
HIROTAKA AKATSUKA
Keyword(s):  
Tensor Products ◽  
Zeta Functions ◽  
Summation Formula ◽  
Poisson Summation Formula ◽  
Euler Product ◽  
Multiple Zeta ◽  
Product Expression ◽  
Triple Zeta ◽  
Sine Functions ◽  
Poisson Summation

We construct multiple zeta functions considered as absolute tensor products of usual zeta functions. We establish Euler product expressions for triple zeta functions [Formula: see text] with p, q, r distinct primes, via multiple sine functions by using the signatured Poisson summation formula. We also establish Euler product expressions for triple zeta functions [Formula: see text] with a prime p, via the theory of multiple sine functions.

scholarly journals Some Finite Analogues of the Poisson Summation Formula

1961 ◽  
Vol 12 (3) ◽  
pp. 133-138 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Summation Formula ◽  
Poisson Summation Formula ◽  
Euler’S Constant ◽  
Image Position ◽  
Positive Integers ◽  
Euler's Constant ◽  
Poisson Summation

1. Guinand (2) has obtained finite identities of the typewhere m, n, N are positive integers and eitherorwhere γ is Euler's constant and the notation ∑′ indicates that when x is integral the term r = x is multiplied by ½. Clearly there is no loss of generality in taking N = 1 in (1.1).

scholarly journals A strong version of Poisson summation

1997 ◽  
Vol 20 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Nelson Petulante
Keyword(s):  
Summation Formula ◽  
Poisson Summation Formula ◽  
Strong Version ◽  
Poisson Summation

We establish a generalized version of the classical Poisson summation formula. This formula incorporates a special feature called “compression”, whereby, at the same time that the formula equates a series to its Fourier dual, the compressive feature serves to enable both sides of the equation to converge.

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