scholarly journals Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, 𝔽q) and PGL(2, 𝔽q)

2016 ◽  
Vol 57 (3) ◽  
pp. 031701
Author(s):  
Ph. Roche
Keyword(s):  
Zeta Function ◽  
Function Representation ◽  
Yang Mills ◽  
Generalized Zeta Function

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

scholarly journals An integral involving the generalized zeta function

1990 ◽  
Vol 13 (3) ◽  
pp. 453-460 ◽  
Author(s):  
E. Elizalde ◽  
A. Romeo
Keyword(s):  
Positive Integer ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Riemann Surfaces ◽  
The Riemann Zeta Function ◽  
Special Integral ◽  
Riemann Zeta ◽  
Compact Riemann Surfaces ◽  
Determinants Of Laplacians ◽  
Generalized Zeta Function

A general value for∫abdtlogΓ(t), fora,bpositive reals, is derived in terms of the Hurwitzζfunction. That expression is checked for a previously known special integral, and the case whereais a positive integer andbis half an odd integer is considered. The result finds application in calculating the numerical value of the derivative of the Riemann zeta function at the point−1, a quantity that arises in the evaluation of determinants of Laplacians on compact Riemann surfaces.

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