Shintani’s prehomogeneous zeta functions and multiple sine functions

2005 ◽  
Vol 54 (3) ◽  
pp. 303-311
Author(s):  
Nobushige Kurokawa
Keyword(s):  
Zeta Functions ◽  
Sine Functions

Extensions of Zeta Functions ? Examples and a Study of the Double Sine Functions

2005 ◽  
Vol 86 (1-2) ◽  
pp. 179-201
Author(s):  
Nobushige Kurokawa ◽  
Masato Wakayama
Keyword(s):  
Zeta Functions ◽  
Sine Functions

ITERATED EULER'S INTEGRALS AND NORMALIZED MULTIPLE SINE FUNCTIONS

2009 ◽  
Vol 20 (09) ◽  
pp. 1147-1157
Author(s):  
HIDEKAZU TANAKA
Keyword(s):  
Zeta Functions ◽  
Type Formula ◽  
Basic Properties ◽  
Sine Functions

We introduce iterated Euler's integrals, and we give expressions using zeta functions. Moreover, we prove that normalized multiple sine functions are expressed via iterated Euler's integrals. Then, we show basic properties of multiple sine functions from these results containing Kummer type formula.

PERIOD DEFORMATIONS OF MULTIPLE HURWITZ ZETA FUNCTIONS

2007 ◽  
Vol 18 (07) ◽  
pp. 809-820 ◽  
Author(s):  
KAZUHIRO ONODERA
Keyword(s):  
Zeta Functions ◽  
Sine Functions

We study continuous period deformations of the multiple Hurwitz zeta functions and their derivatives. Moreover we investigate period deformations of the generalized multiple gamma and sine functions and give applications.

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.

ASYMPTOTIC EXPANSIONS FOR PERIOD DEFORMATIONS OF MULTIPLE HURWITZ ZETA FUNCTIONS AND THEIR ASSOCIATED FUNCTIONS

2009 ◽  
Vol 20 (03) ◽  
pp. 299-307
Author(s):  
KAZUHIRO ONODERA
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Expansions ◽  
Zeta Functions ◽  
Associated Functions ◽  
Sine Functions

We study the asymptotic behavior of multiple Hurwitz zeta functions and generalized multiple gamma and sine functions as some period parameters tend to 0. We obtain the perfect asymptotic expansions and get some applications in refining a previous paper by the author.

scholarly journals Zeta functions and normalized multiple sine functions

2005 ◽  
Vol 28 (3) ◽  
pp. 534-550 ◽  
Author(s):  
Shin-ya Koyama ◽  
Nobushige Kurokawa
Keyword(s):  
Zeta Functions ◽  
Sine Functions
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