Riemann ϖ function

The Riemann ϖ function is used in the proof of the analytic continuation for the Riemann Xi function to the whole complex planeMathworldPlanetmath. It is defined as:


This function is a special case of a Jacobi ϑ function (http://planetmath.org/JacobiVarthetaFunctions):


As such the ϖ function satisfies a functional equation, which a special case of Jacobi’s Identity for the ϑ function (http://planetmath.org/JacobisIdentityForVarthetaFunctions).

Title Riemann ϖ function
Canonical name RiemannvarpiFunction
Date of creation 2013-03-22 13:24:12
Last modified on 2013-03-22 13:24:12
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 12
Author rspuzio (6075)
Entry type Definition
Classification msc 11M06