On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function

Abstract

We derive new results about properties of the Witten zeta function associated with the group SU(3), and use them to prove an asymptotic formula for the number of n-dimensional representations of SU(3) counted up to equivalence. Our analysis also relates the Witten zeta function of SU(3) to a summation identity for Bernoulli numbers discovered in 2008 by Agoh and Dilcher. We give a new proof of that identity and show that it is a special case of a stronger identity involving the Eisenstein series.

To appear in Acta Arithmetica

References in corpus (1)

• Mean value theorems for the double zeta-function

Cited by in corpus (3)

• A robust quantitative local central limit theorem with applications to enumerative combinatorics and random combinatorial structures
• An asymptotic formula for the number of $n$-dimensional representations of $\mathrm{SU}(3)$
• Values and derivative values at nonpositive integers of generalized multiple Hurwitz zeta functions