Geodesic
On the number of $n$-dimensional representations of $\operatorname{SU}(3)$, the Bernoulli numbers, and the Witten zeta function
Dan Romik 1
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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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     journal = {Acta Arithmetica},
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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

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