• The theta correspondence 1 is a correspondence between automorphic forms on two members of a dual reductive pair. Because of the relation between automorphic forms and automor-phic representations, it is also a correspondence between automorphic representations. The Siegel-Weil formula says that certain natural linear combinations of theta lifts are Siegel-type holomorphic Eisenstein Series.

The almost automorphic solution is a generalization of the almost periodic solution. In this paper, the almost automorphic solutions of Cohen-Grossberg neural networks with delays are considered. Using the semi-discretization method and the contraction mapping principle, some sufficient conditions are obtained to ensure the existence and the uniqueness of almost automorphic solutions to Cohen-G...

The automorphic representation associated to an eigenform will be described, as well as its local factors at the places of F. The statement that the local factor of the automorphic representation determines the local Galois representation (after F-semisimplification) will be explained, and an explicit description will be given in at least the case of a principal series local representation. The...

An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatments of matter and antimatter in due time, in this paper we present a classical represe...

Two dimensional adelic objects were introduced by I. Fesenko in his study of the Hasse zeta function associated to a regular model E of the elliptic curve E. The Hasse-Weil L-function L(E, s) of E appears in the denominator of the Hasse zeta function of E . The two dimensional adelic analysis predicts that the integrand h of the boundary term of the two dimensional zeta integral attached to E i...

I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level G(Ẑ) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic f...

1.1 There is a well known procedure which associates to any cusp formfon the congruence subgroup Fo(N) of SL2(2g), which is an eigenform for the Hecke algebra, a representation a(f) of Gal(ff~/ll)) on a two dimensional vector space over a finite extension of I1~ (for any prime number l) [D]. Moreover, one has an equality of L-series: L (f, s)=L (o'(f), s). In case the weight of f is 2, this Gal...

In the paper ‘Automorphic functions for a Whitehead-complement group’ [5], Matsumoto, Nishi and Yoshida constructed automorphic functions on real 3–dimensional hyperbolic space for a Kleinian group called the Whitehead-link-complement group. For a Kleinian group (of the first kind), no automorphic function/form has been studied before. In this note, their motivation is presented with a historic...

Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces automorphic forms. We prove unitarity ``Langlands element'' (i.e., representation specified by Arthur) all unipotent Arthur packets for split real exceptional groups. The proof uses Eisenstein series, Langlands' constant term formula and square integrability criterion, analytic proper...