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.