Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Wszystkie zeszyty

Streszczenie

We derive new results about properties of the Witten zeta function associated with the group ${\rm SU }(3)$, and use them to prove an asymptotic formula for the number of $n$-dimensional representations of ${\rm SU }(3)$ counted up to equivalence. Our analysis also relates the Witten zeta function of ${\rm SU} (3)$ 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.