Explicit formulae for L-functions: Difference between revisions

Revision as of 19:50, 26 May 2020

Revision as of 21:03, 26 May 2020

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*The terms on the right hand side come from the logarithmic derivative of

:: <math>\zeta^*(s)= \Gamma(s/2)\pi^{-s/2}\prod_p \frac{1}{1-p^{-s}}</math>

:with the terms corresponding to the prime ''p'' coming from the Euler factor of ''p'', and the term at the end involving Ψ&Psi; coming from the gamma factor (the Euler factor at infinity).

*The left-hand side is a sum over all zeros of ''ζ''^&nbsp;* counted with multiplicities, so the poles at 0 and 1 are counted as zeros of order &minus;1.