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Zeta Regularization Techniques with Applications
Part 1 The Riemann Zeta function: Riemann, Hurwitz, Epstein, Selberg and related zeta functions analytic continuation - practical uses for series summation asymptotic expansion of "zeta". Part 2
Ten Physical Applications of Spectral Zeta Functions
Introduction and Outlook.- Mathematical Formulas Involving the Different Zeta Functions.- A Treatment of the Non-Polynomial Contributions: Application to Calculate Partition Functions of Strings and
One-loop f(R) gravity in de Sitter universe
Motivated by the dark energy issue, the one-loop quantization approach for a family of relativistic cosmological theories is discussed in some detail. Specifically, general f(R) gravity at the
Observational constraints on dark energy with generalized equations of state
We investigate the effects of viscosity terms depending on the Hubble parameter and its derivatives in the dark energy equation of state. Such terms are possible if dark energy is a fictitious fluid
Casimir energies for spherically symmetric cavities
A general calculation of Casimir energies - in an arbitrary number of dimensions - for massless quantized fields in spherically symmetric cavities is carried out. All the most common situations,
Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem
Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, f(G), is added to the general relativity action. We show that a
Class of viable modified f(R) gravities describing inflation and the onset of accelerated expansion
A general approach to viable modified f(R) gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with
Zeta-Function Regularization, the Multiplicative Anomaly and the Wodzicki Residue
Abstract:The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators V1=−Δ+V1 and V2=−Δ+V2, with V1, V2 constant, in a
Zeta function determinant of the Laplace operator on theD-dimensional ball
We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for
On the zeta‐function regularization of a two‐dimensional series of Epstein–Hurwitz type
As a further step in the general program of zeta‐function regularization of multiseries expressions, some original formulas are provided for the analytic continuation, to any value of s, of