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→Gamma function–Legendre function: formula, not function, the trivial character is a Dirichlet character |
→Bernoulli map: Chowla-Selberg redux |
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:<math>\frac{1}{k}\sum_{n=0}^{k-1}g\left(\frac{x+n}{k}\right)=f(k)g(x)</math>
That is, ''g''(''x'') is an eigenfunction of Bernoulli transfer operator, with eigenvalue ''f''(''k''). The multiplication theorem for the Bernoulli polynomials then follows as a special case of the multiplicative function <math>f(n)=n^{-s}</math>. The [[Dirichlet character]]s are fully multiplicative, and thus can be readily used to obtain additional identities of this form.
==Characteristic zero==
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