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MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation
Seminar
Thursday, 5 February 2004, at 15:15 in Kol A4
Nikolai Proskurin
Mathematical Institute, Sankt Petersburg, Russia.
On metaplectic forms with special reference to the cubic case and to the Whittaker functions related

Abstract
By metaplectic forms we understand automorphic forms with certain factors of automorphy constructed by means of residue symbols. The classical example is the quadratic theta function, whose automorphy properties are known after Jacoby. That is a metaplectic form of degree 2. To define metaplectic forms of higher degree one needs factors of automorphy discovered by T. Kubota in 1965 and (in more general context) by Bass, Milnor and Serre in 1967. By studying metaplectic forms we find higher degree analogues of classical theta series. One of them is the Kubota-Patterson cubic theta function studied in details by S.J. Patterson in 1977. The theory we talk about gives rise to solution of two old problems. That are Kummer's problem on cubic Gauss sums and the congruence subgroup problem for general linear and symplectic groups.

Contact person:Alexei Venkov.