Kronecker Limit Formulas for the Mordell-Tornheim Zeta Function
The Mordell-Tornheim zeta function is a multiple Dirichlet series in several complex arguments, and its Kronecker-limit-type formulas describe the singular and constant parts of its Laurent expansion as one argument approaches a pole. Students learn how such formulas locate the poles and their orders and how a single deformation of this zeta function unifies many classical modular relations - those of Herglotz, Ramanujan, Guinand and Zagier - together with series evaluations via the Herglotz-Zagier function and a family of mixed functional equations.
THE MORDELL-TORNHEIM ZETA FUNCTION: KRONECKER LIMIT TYPE FORMULA, SERIES EVALUATIONS AND
The Mordell-Tornheim zeta function is a multiple Dirichlet series in three complex arguments; the authors study a one-parameter deformation Theta(r,s,t,x) that reduces to it at x=1 and satisfies simp…