Related papers: A database of rigorous Maass forms

Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…

We define the counting function for non-analytic (Maass) newforms of Hecke congruence groups_Gamma_0(M)_. We then calculate the three main terms of this counting function and give necessary and sufficient conditions on M for this counting…

Graph databases have emerged as the fundamental technology underpinning trendy application domains where traditional databases are not well-equipped to handle complex graph data. However, current graph databases support basic graph…

As of 2005, sampling has been incorporated in all major database systems. While efficient sampling techniques are realizable, determining the accuracy of an estimate obtained from the sample is still an unresolved problem. In this paper, we…

We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…

The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group PSL(2,Z) with general multiplier systems and real weight. A selection of numerical results obtained with these…

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).

This paper clarifies the main research methods and ideas of the thesis [1,2,4]. The special calculation process is also realized by corresponding computer algorithm. Finally, we introduce zero rows sum case and give the corresponding…

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

We give several algorithms addressing computations of intersections of conjugate subgroups.

Gamma process has been extensively used to model monotone degradation data. Statistical inference for the gamma process is difficult due to the complex parameter structure involved in the likelihood function. In this paper, we derive a…

Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup \Gamma^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that…

We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.

There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence…

In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…

A database of abstract groups has been added to the L-functions and Modular Forms Database (LMFDB), available at https://www.lmfdb.org/Groups/Abstract/. We discuss the functionality of the database and what makes it distinct from other…

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type…

I present a simple dynamic programming algorithm for the evaluation of operators in a wide range of superconformal algebras. Special care is taken to describe the computation of the Gram matrix. A Mathematica package, Weaver.m, is provided…

We discuss the best methods available for computing the gamma function $\Gamma(z)$ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small…