Related papers: Lamprecht-Tate Formula

Deligne's conjecture is the Lefschetz trace formula for correspondences defined over a finite field. In this paper, we prove an analogous statement of Deligne's conjecture with respect to $p^n$-torsion \'etale cohomology under certain…

This paper refers to Langlands' big set of notes [L] devoted to the question if the (normalized) local Hecke-Tate root number $\Delta=\Delta(E,\chi)$, where $E$ is a finite separable extension of a fixed non-archimedean local field $F$, and…

Series acceleration formulas are obtained for Dirichlet series with periodic coefficients. Special cases include Ramanujan's formula for the values of the Riemann zeta function at the odd positive integers exceeding two, and related…

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of…

We prove an analogue of Deligne's period conjecture for the special value of the L-function of an abelian variety over a global function field twisted by an Artin representation. We illustrate this in action for an example of an elliptic…

Let $\pi$ be a simple supercuspidal representation of the quasi-split unramified even unitary group with respect to an unramified quadratic extension $E/F$ of $p$-adic fields. We compute the Rankin-Selberg gamma factor for rank-$1$ twists…

We recast the local factors of the Hasse-Weil zeta function at infinity in terms of the Cuntz-Pimsner algebras. The nature of such factors is an open problem studied by Deninger and Serre.

Let E/F be a quadratic extension of p-adic fields. The local Langlands correspondence establishes a bijection between n-dimensional Frobenius semisimple representations of the Weil-Deligne group of E and smooth, irreducible representations…

On the basis of analysis on the adele ring of any algebraic numbers field (Tate's formula) a regularization for divergent adelic products of gamma- and beta-functions for all completions of this field are proposed, and corresponding…

We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac…

Observing that the logarithm of a product of two elliptic operators differs from the sum of the logarithms by a finite sum of operator brackets, we infer that regularised traces of this difference are local as finite sums of noncommutative…

This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…

The local Tamagawa number conjecure, first formulated by Fontaine and Perrin-Riou, expresses the compatibility of the (global) Tamagawa number conjecture on motivic $L$-functions with the functional equation. The local conjecture was proven…

Let $f\colon X\to\mathbb{A}^1_k$ be a morphism from a smooth variety to an affine line with an isolated singular point. For such a singularity, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other…

Simple unsmoothed formulas to compute the Riemann zeta function, and Dirichlet $L$-functions to a power-full modulus, are derived by elementary means (Taylor expansions and the geometric series). The formulas enable square-root of the…

In the paper we prove an explicit formula for the central values of certain Rankin L-functions. These L-functions are L-functions of Hilbert newforms over a totally real field F, twisted by unitary Hecke characters of a totally imaginary…

We obtain an adaptation of Dade's Conjecture and Sp\"ath's Character Triple Conjecture to unipotent characters of simple, simply connected finite reductive groups of type $\bf{A}$, $\bf{B}$ and $\bf{C}$. In particular, this gives a precise…

For an elliptic curve $E$ over a local field $K$ and a separable quadratic extension of $K$, motivated by connections to the Birch and Swinnerton-Dyer conjecture, Kramer and Tunnell have conjectured a formula for computing the local root…

We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its…

In 1938 E. T. Bell introduced "The Iterated Exponential Integers". He proved that these numbers may be expressed by polynomials with rational coefficients. However, Bell gave no formulas for any of the coefficients except the trivial one,…