In Mathematical, the formula of Chowla-Selberg is the evaluation of a certain product of values of the Fonction gamma with the rational values . The name comes from a common paper of 1967 of the Mathématicien S Chowla and Selberg. The basic result was already known earlier in a work of the Czech mathematician Mathias Lerch (1860 - 1922).

In a form logarithmic curve, the formula shows that in certain cases, the sum

can be evaluated (by the theory of the modular forms). Here $\backslash \; chi$ is the Symbole of Jacobi modulo D , where - D is the Discriminant of a quadratic Corps imaginary. The sum is taken on 0 < R < D , with usual convention $\backslash \; chi\; (R)\; =\; 0$ if R and D has a common factor.

The origin of this kind of formulas is now perceived in the theory of the Multiplication complexes, and in particular in the theory of the periods of a abelian Variété of type CM. This led to many research and generalizations. In particular, with the analog of the p-adic numbers, implying a p-adic Function gamma, which was initiated by Gross and Koblitz, an important notion in the theory of the p-adic periods.