Related papers: Character sum, reciprocity and Voronoi formula

An explicit quantization of Chern-Simons theory leads to an identity between sums of the Kac-Weyl characters. One can use this identity to prove inequalities that constrain the fusion coefficients $N_{\mu\nu}^l$ in the case of RCFTs that…

The mock theta conjectures are ten identities involving Ramanujan's fifth-order mock theta functions. The conjectures were proven by Hickerson in 1988 using q-series methods. Using methods from the theory of harmonic Maass forms,…

In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…

A new sums-of-tails identity involving two parameters $b$ and $d$ is obtained and is used to derive more results of similar type. One of Ramanujan's sums-of-tails identities from the Lost Notebook is shown to be a special case of our…

We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi)simple algebra over Q. Our method is based on a generalisation of Vorono\"i's algorithm for computing perfect forms,…

In this paper we resolve a question by Bringmann, Lovejoy, and Rolen on a new vector-valued $U$-type function. We obtain an expression for a corresponding family of Hecke-Appell-type sums in terms of mixed mock modular forms; that is, we…

Using $\ell$-adic cohomology of tensor inductions of lisse $\overline{\mathbb Q}_\ell$-sheaves, we study a class of incomplete character sums.

A recent result of Cohen and Zemel provides an elegant expansion of the Rasala polynomials for symmetric group character degrees. In this note we present an alternative short algebraic proof. Extensions to polynomials of character values…

We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…

We show in a quantitative way that any odd character $\chi$ modulo $q$ of fixed order $g \geq 2$ satisfies the property that if the P\'{o}lya-Vinogradov inequality for $\chi$ can be improved to $$\max_{1 \leq t \leq q} \left|\sum_{n \leq t}…

Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let $\gf_{p^m}$ be the finite field with $p^m$ elements for a prime $p$ and a positive integer $m$. Let…

In this article, we investigate conditional large values of quadratic Dirichlet character sums. We prove some Omega results of quadratic character sums under the assumption of the generalized Riemnn hypothesis, which are as sharp as…

In this article, we use Lindstr\"om Gessel Viennot Lemma to give a short, combinatorial, visualizable proof of the identity of Schur polynomials -- the sum of monomials of Young tableaux equals to the quotient of determinants. As a…

We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as a reciprocity formula for cotangent sums, related to the…

We show that certain sums studied in two recent papers are basically character coordinates (as they are called in the literature). These sums involve values of Dirichlet characters and powers of $\cot(\pi k/n)$, $1\le k\le n-1$. We also…

The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth…

It was shown in that harmonic numbers satisfy certain reciprocity relations, which are in particular useful for the analysis of the quickselect algorithm. The aim of this work is to show that a reciprocity relation from…

In this thesis we construct a modified version of Karoubi's relative Chern character for smooth varieties over the complex numbers or the ring of integers in a p-adic number field. Comparison results with the Deligne-Beilinson Chern…

In this article, we investigate the variance of local $\varepsilon$-factor for a modular form with arbitrary nebentypus with respect to twisting by a quadratic character. We detect the type of the supercuspidal representation from that. For…

We give an elementary proof of a Caratheodory-type result on the invertibility of a sum of matrices, due first to Facchini and Barioli. The proof yields a polynomial identity, expressing the determinant of a large sum of matrices in terms…