Multiple Dirichlet series

Recently Diaconu, Goldfeld, and Hoffstein [ arXiv:math.NT/0110092] have considered mean values similar to those described in the article on shifted zeta functions. They refer to these as ``Multiple Dirichlet Series.''

These mean values are viewed as functions of several complex variables, and they make a precise conjecture about the polar divisors of the function. Furthermore, they prove that their conjecture on the polar divisors implies the truth of the conjectured mean values which have been obtained from random matrix theory.

These techniques extend to the case of ratios of zeta functions, and also are applicable to mean values of $L$-functions with other symmetry types.

(A more extensive description is in preparation).

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