## Abstract

In this paper, we discuss mean values of some Witten *L*-functions with respect to the “character aspect”. In particular, we focus on the $\mathrm{SU}(2)$ case. We prove that such mean values turn out to be 0, 1 or to diverge.

Show Summary Details# Mean values of the Witten *L*-function for SU(2)

## Abstract

## References

## About the article

More options …# Forum Mathematicum

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Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898

Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2017: 0.67

- Online
- ISSN
- 1435-5337

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Get Access to Full TextIn this paper, we discuss mean values of some Witten *L*-functions with respect to the “character aspect”. In particular, we focus on the $\mathrm{SU}(2)$ case. We prove that such mean values turn out to be 0, 1 or to diverge.

Keywords: Witten zeta function

MSC 2010: 11M32

- [1]
Apostol T. M., Polylogarithm, NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge (2010), 611–612. Google Scholar

- [2]
González-Sánchez J., Jaikin-Zapirain A. and Klopsch B., The representation zeta function of a FAb compact

*p*-adic Lie group vanishes at -2, Bull. Lond. Math. Soc. 46 (2014), 239–244. Google Scholar - [3]
Jonquière A., Note sur la série ${\sum}_{n=1}^{\mathrm{\infty}}\frac{{x}^{n}}{{n}^{s}}$, Bull. Soc. Math. France 17 (1889), 142–152. Google Scholar

- [4]
Koyama S. and Kurokawa N., Triple mean values of Witten

*L*-functions, Monatsh. Math. (2015), 10.1007/s00605-015-0841-5. Google Scholar - [5]
Kurokawa N. and Ochiai H., Zeros of Witten zeta functions and applications, Kodai Math. J. 36 (2013), 440–454. Google Scholar

- [6]
Min J., Zeros and special values of Witten zeta functions and Witten

*L*-functions, J. Number Theory 134 (2014), 240–257. Google Scholar - [7]
Oberhettinger F., Tables of Mellin Transforms, Springer, Berlin, 1974. Google Scholar

- [8]
Witten E., On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), 153–209. Google Scholar

**Received**: 2015-03-25

**Revised**: 2015-10-04

**Published Online**: 2016-06-10

**Published in Print**: 2017-03-01

**Citation Information: **Forum Mathematicum, Volume 29, Issue 2, Pages 457–464, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0056.

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