Related papers: Lamprecht-Tate Formula

In this article, we obtain a transformation formula for the higher power of odd zeta values, which generalizes Ramanujan's formula for odd zeta values. We have also investigated many important applications, which in turn provide…

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As…

This paper gives combinatorial formulas for discrete series constants, both stable and unstable, on real reductive groups. It also carries out one step of the comparison of the topological trace formula for Hecke operators with Arthur's…

Consider exponential Carmichael function $\lambda^{(e)}$ such that $\lambda^{(e)}$ is multiplicative and $\lambda^{(e)}(p^a) = \lambda(a)$, where $\lambda$ is usual Carmichael function. We discuss the value of $\sum \lambda^{(e)}(n)$, where…

Using Borevich's system of generators and relations, the classical Artin-Hasse formula is obtained from scratch in the case when taking $p$-th root of the second argument of the Hilbert symbol gives an unramified $p$-extension of the same…

Let $G$ be the group of rational points of a general linear group over a non-archimedean local field $F$. We show that certain representations of open, compact-mod-centre subgroups of $G$, (the maximal simple types of Bushnell and Kutzko)…

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…

We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$…

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules…

For a fixed integer $t \geq 2$, we consider the irreducible characters of representations of the classical groups of types A, B, C and D, namely $\text{GL}_{tn}, \text{SO}_{2tn+1}, \text{Sp}_{2tn}$ and $\text{O}_{2tn}$, evaluated at…

A detailed analysis of the remainder obtained by truncating the Euler series up to the $n$th-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse…

We prove a sum-shuffle formula for multiple zeta values in Tate algebras (in positive characteristic), introduced in \cite{PEL3}.This follows from an analog result for double twisted power sums, implying that an ${\mathbb{F}\_p$-vector…

Plouffe conjectured rapidly converging series formulas for $\pi^{2n+1}$ and $\zeta (2n+1)$ for small values of $n$. We find the general pattern for all nonnegative integer values of $n$ and offer a proof.

We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet $L$-functions, $L(1/2,\chi_d)$, and also of the $L$-functions associated to quadratic twists of an…

We give a purely combinatorial derivation of Littelmann's refined Demazure character formula

We provide a formula for the order of the Tate--Shafarevich group of elliptic curves over dihedral extensions of number fields of order $2n$, up to $4^{th}$ powers and primes dividing $n$. Specifically, for odd $n$ it is equal to the order…

We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called…

The goal of this note is to show that in the case of transversal intersections the "true local terms" appearing in the Lefschetz trace formula equal to the "naive local terms". To prove the result we extend the method of [Va], where the…

A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…

We establish an explicit Plancherel decomposition for $\mathrm{GL}_n(F)\backslash \mathrm{GL}_n(E)$ where $E/F$ is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai…