Vol. 31 (2021)
Articles

A note in the Riemann \(\xi - \) Function

M.L. Glasser
Department of Physics, Clarkson University, Potsdam, NY, U.S.A. Departamento de F´ısica Teorica, ´Universidad de Valladolid, Spain.

Publicado 2024-07-11

Palabras clave

  • Integral equations,
  • \(\xi - \) Function,
  • \( zeta -\) Function

Resumen

This note investigates a number of integrals of and integral equations satisfied by Riemann’s \(\ xi - \) function and its integer powers.

A somewhat less restrictive derivation of one of Riemann’s identities is provided. The work centers on the critical strip and it is argued that the line   \(\ s = 3/2 + it \, , \, \text{e.g.,}\)  contains a kind of holographic image of the critical region.