Explicit formulae for L-functions: Difference between revisions

Revision as of 20:06, 26 September 2020

Revision as of 20:07, 26 September 2020

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for the divisor function of zeroth order <math> \sum_{n=1}^\infty \sigma_0 (n) f(n) = \sum_ {m=-\infty}^\infty \sum_{n=1}^\infty f(mn) </math>

using a test function of the form <math> f(xeye^{x})e^{ax} </math> for some positive 'a' turns the poisson summation formula into a formula involving the Mellin transform , here 'y' is a real parameter

==Generalizations==