Theta functions and arithmetic quotients of loop groups

Theta functions on covers of symplectic groups

We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$‎. ‎This representation is obtained from the residues of Eisenstein series on this group‎. ‎If $r$ is odd‎, ‎$nle r

Compactness of arithmetic quotients of anisotropic orthogonal groups

where | ∗ |v is the v from among the normalization of norms so that the product formula holds. A vector x ∈ VA is primitive if it is of the form xog where g ∈ GL(n,A) and xo ∈ VQ. That is, it is an image of a rational point of the vectorspace by an element of the adele group. For x = (x1, . . . , xn) ∈ VQ, at almost all non-archimedean primes v the xi’s are in Zv and have greatest common diviso...

Arithmetic theta lifting and L-derivatives for unitary groups, I

Arithmetic theta lifting and L-derivatives for unitary groups, II

Braids, Galois Groups, and Some Arithmetic Functions

This lecture is about some new relations among the classical objects of the title. The study of such relations was started by [Bi, G, De, Ihj] from independent motivations, and was developed in [A3, C3, A-I, IKY, Dr2, O, N], etc. It is still a very young subject, and there are several different approaches, each partly blocked by its own fundamental conjectures! But it is already allowing one to...