For ψ a nontrivial additive character on the finite field Fq, observe that the map t 7→ P x∈Fq ψ(f(x) + tx) is the Fourier transform of the map t 7→ ψ(f(t)). As is well-known, this has a cohomological interpretation, producing a continuous l-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both l-adic and p-adic meth...

We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of more general graphs. The connection with generic exchange Hamiltonians in quantum mechanics is discussed in an appendix.

assume H : Rn → R is an invariant or the energy of the system, and that we have f(y) = S∇H(y) with S an n× n, skew-symmetric matrix1. To derive energy-preserving numerical integration methods for these problems one can use discrete gradient techniques, [5], [7]. Such methods rely on appropriate approximations of∇H(y) and S (in the case S depends on y), and in general can not be expanded in a B-...

We compute the arithmetic L-invariants (of Greenberg–Benois) of twists of symmetric powers of p-adic Galois representations attached to Iwahori level Hilbert modular forms (under some technical conditions). Our method uses the automorphy of symmetric powers and the study of analytic Galois representations on p-adic families of automorphic forms over symplectic and unitary groups. Combining thes...

Plethysm, introduced by Littlewood, is an operation on symmetric functions that corresponds to composition of Schur and or Weyl functors. Let R be a commutative ring with identity and F a free R-module of finite rank. We denote by 4F, SF, and DF the exterior, symmetric, and divided power algebra of F, respectively. Over the last decade or so, a number of authors have studied plethysms of type A...

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...

In this paper, we propose a high-performance parallel three-dimensional fast Fourier transform (FFT) algorithm on clusters of vector symmetric multiprocessor (SMP) nodes. The three-dimensional FFT algorithm can be altered into a multirow FFT algorithm to expand the innermost loop length. We use the multirow FFT algorithm to implement the parallel three-dimensional FFT algorithm. Performance res...

1. Introduction In this paper we consider some results on the orbits of groups of collineations, or, more generally, on the point and block classes of tactical decompositions, on symmetric balanced incomplete block designs (symmetric BIBD = (v, k, 2)-system=finite 2-plane), and we consider generalizations to (not necessarily symmetric) BIBD and other combinatorial designs. The results are about...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...

in this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. the fgm shell with ring is developed in accordance to the volume fraction law from two constituents namely stainless steel and nickel. these constituents are graded th...