Geodesic
On the number of $n$-dimensional representations of $\operatorname{SU}(3)$, the Bernoulli numbers, and the Witten zeta function
Dan Romik1
1 Department of Mathematics University of California, Davis One Shields Ave. Davis, CA 95616, U.S.A.
Acta Arithmetica, Tome 180 (2017) no. 2, pp. 111-159.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa8455-3-2017
Keywords: derive results about properties witten zeta function associated group prove asymptotic formula number n dimensional representations counted equivalence analysis relates witten zeta function summation identity bernoulli numbers discovered agoh dilcher proof identity special stronger identity involving eisenstein series

Dan Romik 1

1 Department of Mathematics University of California, Davis One Shields Ave. Davis, CA 95616, U.S.A. 
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Dan Romik. On the number of $n$-dimensional representations of $\operatorname{SU}(3)$, the Bernoulli numbers, and the Witten zeta function. Acta Arithmetica, Tome 180 (2017) no. 2, pp. 111-159. doi : 10.4064/aa8455-3-2017. http://geodesic.mathdoc.fr/articles/10.4064/aa8455-3-2017/

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