Related papers: Integrals derived from the doubling method

The study of the global mapping properties of arbitrary Dirichlet L-functions is undertaken. The results are applied to the proof of the Generalized Riemann Hypothesis.

The aim of this article is to study rank-one Eisenstein cohomology for the group GL(N)/F, where F is a totally real field extension of Q. This is then used to prove rationality results for ratios of successive critical values for…

In this article we show analytic properties of certain Rankin-Selberg type Dirichlet series for holomorphic Jacobi cusp forms of integral weight and of half-integral weight. The numerators of these Dirichlet series are the inner products of…

We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel'fand and Dikii, the Skolem-Mahler-Lech…

We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial…

We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and…

We introduce a self-inverse function via an integral equivalent to a two-term combination of dilogarithms. We refer to this function as a fundamental form, since there is a family of extensions of this function that satisfy similar…

We use the exterior product of double forms to reformulate celebrated classical results of linear algebra about matrices and bilinear forms namely the Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and…

Let $n$ and $n'$ be positive integers such that $n-n'\in \{0,1\}$. Let $F$ be either $\mathbb{R}$ or $\mathbb{C}$. Let $K_n$ and $K_{n'}$ be maximal compact subgroups of $\mathrm{GL}(n,F)$ and $\mathrm{GL}(n',F)$, respectively. We give the…

We generalise well-known integrals of Ingham-Siegel and Fisher-Hartwig type over the unitary group $U(N)$ with respect to Haar measure, for finite $N$ and including fixed external matrices. When depending only on the eigenvalues of the…

We extend the theory of local constants to l-adic families of representations of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta integrals and gamma factors for representations coming from the conjectural "local…

A well-known principle states that a congruence between objects should give rise to a corresponding congruence between the special values of $L$-functions attached to these objects. In this article, using the machinery of Eisenstein…

In this note, we introduce a new concept of a {\it generalized algebraic rational identity} to investigate the structure of division rings. The main theorem asserts that if a non-central subnormal subgroup $N$ of the multiplicative group…

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of…

In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of…

Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for $\hat{\goth{sl}(2)}$ satisfy certain classical recursion formulas…

We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules defined over the polynomial ring F_q[theta]. This generalizes results of Anderson for the rank one case. As an application we show that certain special…

We first present some identities involving the Pochhammer symbol (rising factorial). We also recall and present some new properties of the Jacobi polynomials. We use them to expand a general hypergeometric function in an orthogonal series…

Recently, Chen, Hou and Jin used both Abel's lemma on summation by parts and Zeilberger's algorithm to generate recurrence relations for definite summations. Meanwhile, they proposed the Abel-Gosper method to evaluate some indefinite sums…

We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra…