All known ways to analytically continue automorphic L-functions involve integral representations using the corresponding automorphic forms. The simplest cases, extending Hecke’s treatment of GL2, need no further analytic devices and very little manipulation beyond Fourier-Whittaker expansions. [1] Poisson summation is a sufficient device for several accessible classes of examples, as in Riemann...

By the relative trace formula approach of Jacquet–Rallis, we prove the global Gan– Gross–Prasad conjecture for unitary groups under some local restrictions for the automorphic representations.

For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...

For us it is imperative not to consider functions on the upper half plane but rather to consider functions on GL(2,Q)\GL(2,A(Q)) where A(Q) is the adéle ring of Q. We also replace Q by an arbitrary number field or function field (in one variable over a finite field) F . One can introduce [3] a space of functions, called automorphic forms, and the notion that an irreducible representation π ofGL...

In this paper existence and asymptotic stability of asymptotically almost automorphic solution of impulsive neural networks with delay is discussed. The results are established by using various fixed point theorems and Lyapunov-like functional. As far as we know, this is the first paper to discuss such kind of solutions for impulsive neural networks. At the end, we give few examples to illustra...

Given graphs H and G, we say that H has a G-Decomposition if we are to partition the edge set of H so that for each part P of the partition, the subgraph of H induced by P is isomorphic to G. Let I(D) be the intersection generated by such a decomposition. We say that D is an automorphic decomposition of H with respect to G if I(D) ∼= H. In this talk, we will show several examples of such a deco...

We introduce the notion of automorphic signatures, which satisfy the following properties: the verification keys lie in the message space, messages and signatures consist of group elements only, and verification is done by evaluating a set of pairing-product equations. These signatures make a perfect counterpart to the powerful proof system by Groth and Sahai (Eurocrypt 2008). We provide practi...

To every right or left Bol loop corresponds a middle loop. In this paper, the cores of loops (RBL) and its corresponding (MBL) were studied. Their algebraic connections considered. It was shown that core RBL is elastic idempotent. The found to be alternative (or idempotent) if only MBL symmetric. If (left) symmetric, then, medial (semimedial). has inverse property (automorphic property, idempot...