Related papers: Calculs effectifs de congruences entre caract\`ere…
We improve a recent result by Shparlinski and Banks related to sums with convolution of Dirichlet characters.
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
In this paper, the congruence equations for caliber and m-caliber in various discriminants are proven. Additionally, We also obtained the lengths of the periods of several continued fractions as corollaries.
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
For an even Dirichlet character psi, we obtain a formula for L(1,psi) in terms of a sum of Dirichlet L-series evaluated at s=2 and s=3 and a rapidly convergent numerical series involving the central binomial coefficients. We then derive a…
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.
We provide a characterisation of strong bisimilarity in a fragment of CCS that contains only prefix, parallel composition, synchronisation and a limited form of replication. The characterisation is not an axiomatisation, but is instead…
Large Language Models (LLMs) are intended to reflect human linguistic competencies. But humans have access to a broad and embodied context, which is key in detecting and resolving linguistic ambiguities, even in isolated text spans. A…
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…
This technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms.…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
The main purpose of this paper is to establish bounds on the second moment of $L\big(\tfrac{1}{2}+it,\chi\big)$, averaged over families of fixed order characters. A discrete version of the main result is also stated, from which zero-density…
We give an improvement of a result of J. Martinet on Stickelberger's congruences for the absolute norms of relative discriminants of number fields, by using classical arguments of class field theory.
In this article, we derive a congruence property of particular sum rules involving prime numbers. The resulting expression involves Bernoulli numbers and polynomials, for which we obtain, as a consequence, a general congruence relation as…
Factual consistency is one of important summary evaluation dimensions, especially as summary generation becomes more fluent and coherent. The ESTIME measure, recently proposed specifically for factual consistency, achieves high correlations…
Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a…
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…
We introduce and investigate a series of matching problems for patterns with variables under Simon's congruence. Our results provide a thorough picture of these problems' computational complexity.
An interesting problem in classical differential geometry is to find methods to prove that two surfaces defined by different charts actually coincide up to position in space. In a previous paper we proposed a method in this direction for…
We compute explicitly traces of the Dirichlet form related to the Bessel process with respect to discrete measures as well as measures of mixed type. Then some global properties of the obtained Dirichlet forms, such as conservativeness,…