Functional equations for regularized zetafunctions and diffusion processes
Abstract
We discuss modifications in the integral representation of the Riemann zetafunction that lead to generalizations of the Riemann functional equation that preserves the symmetry s → (1  s) in the critical strip. By modifying one integral representation of the zetafunction with a cutoff that does exhibit the symmetry x ↦ 1/x, we obtain a generalized functional equation involving Bessel functions of second kind. Next, with another cutoff that does exhibit the same symmetry, we obtain a generalization for the functional equation involving only one Bessel function of second kind. Some connection between one regularized zetafunction and the Laplace transform of the heat kernel for the Euclidean and hyperbolic space is discussed.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2020
 DOI:
 10.1088/17518121/ab8d51
 arXiv:
 arXiv:2004.12723
 Bibcode:
 2020JPhA...53w5205S
 Keywords:

 Riemann zetafunction;
 functional equations;
 diffusion processes;
 Mathematical Physics
 EPrint:
 Version to match the one to appear in Journal of Physics A