Abstract
Mean values of Witten L-functions in the “character” aspect are investigated. After giving a general formula for mean values with the first and the second power, we explicitly calculate the cubic moment for SU(2).
Similar content being viewed by others
References
Bartholodi, L., de la Harpe, P.: Representation zeta functions of wreath products with finite groups. Groups Geom. Dyn. 4, 209–249 (2010)
Brézin, E., Hikami, S.: Characteristic polynomials of random matrices. Commun. Math. Phys. 214, 111–135 (2000)
Conrey, J.B., Ghosh, A.: Mean values of the Riemann zeta-function, III. In: Proceedings of the Amalfi Conference on Analytic Number Theory, Univ. Salerno, Salerno, pp. 35–59 (1992)
Conrey, J.B., Gonek, S.M.: High moments of the Riemann zeta-function. Duke Math. J. 107, 577–604 (2001)
Conrey, J.B., Iwaniec, H.: The cubic moment of central values of automorphic \(L\)-functions. Ann. Math. 151, 1175–1216 (2000)
González-Sánchez, J., Jaikin-Zapirain, A., Klopsch, B.: The representation zeta function of a FAb compact p-adic Lie group vanishes at \(-2\). Bull. Lond. Math. Soc. 46, 239–244 (2014)
Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products, 6th edn. Academic Press, New York (2000)
Hardy, G.H., Littlewood, J.E.: Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes. Acta Math. 41, 119–196 (1918)
Ingham, A.E.: Mean-value theorems in the theory of the Riemann zeta-function. Proc. Lond. Math. Soc. 27(2), 273–300 (1926)
Keating, J.P., Snaith, N.C.: Random matrix theory and \(\zeta (1/2+it)\). Commun. Math. Phys. 214, 57–89 (2000)
Kurokawa, N., Ochiai, H.: Zeros of Witten zeta functions and absolute limit. Kodai Math. J. 36, 440–454 (2013)
Larsen, M., Lubotzky, A.: Representation growth of linear groups. J. Eur. Math. Soc. 10, 351–390 (2008)
Mellin, H.: Eine Formel für den Logarithmus transcendenter Funktionen von endlichen Geschlecht. Acta Soc. Scient. Fennicae 29, 3–49 (1900)
Min, J.: Zeros and special values of Witten zeta functions and Witten \(L\)-functions. J. Number Theory 134, 240–257 (2014)
Witten, E.: On quantum gauge theories in two dimensions. Commun. Math. Phys. 141, 153–209 (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by J. Schoißengeier.
Rights and permissions
About this article
Cite this article
Koyama, Sy., Kurokawa, N. Triple mean values of Witten L-functions. Monatsh Math 181, 405–418 (2016). https://doi.org/10.1007/s00605-015-0841-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-015-0841-5