2 research outputs found
On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function
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.Comment: To appear in Acta Arithmetic