Multiplication theorem: Difference between revisions

Revision as of 23:19, 10 January 2011

Revision as of 12:21, 29 July 2011

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:<math>k^s\,\zeta(s,kz)= \sum_{n=0}^{k-1}\zeta\left(s,z+\frac{n}{k}\right)</math>

and

:<math>\zeta(s,kz)=\sum_sum^{\infty}_{n=0} {s+n-1 \choose n} (1-k)^n z^n \zeta(s+n,z).</math>

Multiplication formulas for the non-principal characters may be given in the form of [[Dirichlet L-function]]s.