Finite integral involving the product of generalized Zeta-function, a class of polynomials and multivariable Aleph-functions

2017 ◽  
Vol 45 (2) ◽  
pp. 117-127
Author(s):  
F.Y Ayant ◽  
Keyword(s):  
Zeta Function ◽  
Finite Integral ◽  
Generalized Zeta Function

scholarly journals Finite Integral Involving the Modified Generalized Aleph-Function of Two Variables Extension and Generalized Extented Hurwitz’s Zeta Function

2021 ◽  
Vol 8 (5) ◽  
pp. 198-212
Author(s):  
Frédéric Ayant ◽  
Prvindra Kumar
Keyword(s):  
Zeta Function ◽  
Finite Integral ◽  
Function Of Two Variables ◽  
Generalized Zeta Function

In the present paper, we evaluate the general finite integral invoving the generalized Zeta function and the modified of generalized Aleph-function of two variables.

scholarly journals ONE-LOOP QUANTUM COSMOLOGICAL CORRECTION TO THE GRAVITATIONAL CONSTANT IN THE CLOSED FRIEDMANN–ROBERTSON–WALKER UNIVERSE

2010 ◽  
Vol 25 (21) ◽  
pp. 4111-4122
Author(s):  
S. JALALZADEH ◽  
F. DARABI
Keyword(s):  
Zeta Function ◽  
Regularization Method ◽  
Gravitational Constant ◽  
Invariance Property ◽  
Shape Invariance ◽  
The One ◽  
Friedmann Robertson Walker ◽  
Fluctuation Potential ◽  
Generalized Zeta Function

In this paper, we calculate the one-loop quantum cosmological corrections to the kink energy in the closed Friedmann–Robertson–Walker universe in which the fluctuation potential V″ has a shape invariance property. We use the generalized zeta-function regularization method to implement our setup for describing quantum kink-like states. It is conjectured that the corrections lead to the renormalized gravitational constant.

scholarly journals The Zeta Function of a Hypergraph

10.37236/1110 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Christopher K. Storm
Keyword(s):  
Zeta Function ◽  
Riemann Hypothesis ◽  
Bipartite Graphs ◽  
Selberg Zeta Function ◽  
Isomorphic Graphs ◽  
Natural Way ◽  
Generalized Zeta Function

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the generalized zeta function can be applied to graphs to distinguish non-isomorphic graphs with the same Ihara-Selberg zeta function.

Generalized zeta-function regularization

1987 ◽  
Vol 30 (5) ◽  
pp. 359-362
Author(s):  
P. M. Lavrov
Keyword(s):  
Zeta Function ◽  
Generalized Zeta Function
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