# On the Sums $$\sum_{k=-\infty}^{\infty} (4k+1)^{-n}$$

by Noam Elkies

Year of Award: 2004

Publication Information: The American Mathematical Monthly, August-September 2003, pp. 561-573.

Summary: This paper interprets the sum in the title as a volume of an n-dimensional polytope which can in turn be related to combinatorial problems.  The sum is relevant to the Euler and Bernoulli numbers that arise in the classical study of the zeta function.