Related papers: Calculs effectifs de congruences entre caract\`ere…
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers,…
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
In this paper we define an integral operator on Lp and obtain its degree of convergence in the appropriate norm. By specializing the kernel of the integral operator we obtain many known results as corollaries. We have also applied our…
This article aims to make explicit the characteristic projection introduced by Panchishkin in "A new method of constructing p-adic L-functions associated with modular forms" (Moscow Mathematical Journal, 2002) and gives various results on…
We report on two machine learning experiments in search of statistical relationships between Dirichlet coefficients and root numbers or analytic ranks of certain low-degree $L$-functions. The first experiment is to construct interpretable…
This paper improves the upper bound for the exceptional zeroes of Dirichlet L-functions with even characters. The result is obtained by improving on explicit estimate for $L'(\sigma;\chi)$ for $\sigma$ close to unity, using a result on the…
We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for…
In this paper we study the convergence of multiple Dirichlet L-series. In particular we give an integral representation of the series in the region of convergence by using Abel's summation formula. A certain generalized result is also…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
This article offers an empirical exploration on the use of character-level convolutional networks (ConvNets) for text classification. We constructed several large-scale datasets to show that character-level convolutional networks could…
In this short note we present a comprehensive bibliography for the online exact string matching problem. The problem consists in finding all occurrences of a given pattern in a text. It is an extensively studied problem in computer science,…
An approximate textual retrieval algorithm for searching sources with high levels of defects is presented. It considers splitting the words in a query into two overlapping segments and subsequently building composite regular expressions…
We calculate murmuration densities for two families of Dirichlet characters. The first family contains complex Dirichlet characters normalized by their Gauss sums. Integrating the first density over a geometric interval yields a murmuration…
We consider $cp_{a,b,m}(n)$, the number of $(a,b,m)$-copartitions of $n$. We find many infinitelymany congruencesmodulo 2 and 6 for some particular value of $a$, $b$ and $m$.
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
We prove a new "Toeplitz exactness" theorem for strong convergence. This is a machine to upgrade strong convergence in the general setting of $C^\ast$-correspondences, and has several applications.
Discourse connectives (e.g. however, because) are terms that can explicitly convey a discourse relation within a text. While discourse connectives have been shown to be an effective clue to automatically identify discourse relations, they…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
This article is a sequel to a recent article by Eric Rowland and Reem Yassawi, presenting yet another approach to the fast determination of congruence properties of `famous' combinatorial sequences. The present approach can be taught to a…
We introduce and study a family of functions we call the "mock characters". These functions satisfy a number of interesting properties, and of all completely multiplicative arithmetic functions seem to come as close as possible to being…