Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

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
See all formats and pricing
More options …
Volume 29, Issue 2

Issues

Mean values of the Witten L-function for SU(2)

Jeongwon Min
  • Corresponding author
  • Tokyo Institute of Technology, Department of Mathematics, Oo-okayama Meguro, Tokyo 152-8551, Japan
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-06-10 | DOI: https://doi.org/10.1515/forum-2015-0056

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 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

References

  • [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 n=1xnns, 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

About the article


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.

Export Citation

© 2017 by De Gruyter.Get Permission

Comments (0)

Please log in or register to comment.
Log in