A5045195686- Polynomial and algebraic computation
- Algebraic Geometry and Number Theory
- Advanced Numerical Analysis Techniques
- Advanced Algebra and Geometry
- Coding theory and cryptography
- Numerical methods for differential equations
- Cryptography and Residue Arithmetic
- Analytic Number Theory Research
- Nonlinear Waves and Solitons
- Commutative Algebra and Its Applications
- Black Holes and Theoretical Physics
- Advanced Differential Equations and Dynamical Systems
- graph theory and CDMA systems
- Advanced Combinatorial Mathematics
- BIM and Construction Integration
- Homotopy and Cohomology in Algebraic Topology
- Advanced Topics in Algebra
- Cryptography and Data Security
- Advanced Mathematical Identities
- Algebraic and Geometric Analysis
- semigroups and automata theory
- Algebraic structures and combinatorial models
- Parallel Computing and Optimization Techniques
- Geometric and Algebraic Topology
- Matrix Theory and Algorithms
Florida State University
2014-2024
Breast International Group
2024
Institut national de recherche en informatique et en automatique
2016
Université Paris-Saclay
2016
Inria Saclay - Île de France
2016
Florida Department of State
2012
Florida A&M University - Florida State University College of Engineering
2011
Framingham State University
2010
Radboud University Nijmegen
1994-1997
We calculate 3-loop master integrals for heavy quark correlators and the QCD corrections to $ρ$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-$N$ space either. The solution homogeneous is possible terms convergent close integer power series as $_2F_1$ Gauß hypergeometric functions at rational argument. In some cases, this type can mapped complete elliptic This class appears next one arising...
The Riemann theta function is a complex-valued of $g$ complex variables. It appears in the construction many (quasi-)periodic solutions various equations mathematical physics. In this paper, algorithms for its computation are given. First, formula derived allowing pointwise approximation functions, with arbitrary, user-specified precision. This used to construct uniform formula, again arbitrary
Let $K$ be a number field, and let $E/K$ an elliptic curve over $K$. The Mordell--Weil theorem asserts that the $K$-rational points $E(K)$ of $E$ form finitely generated abelian group. In this work, we complete classification finite groups which appear as torsion subgroup for cubic field. To do so, determine on modular curves $X_1(N)$ \[N = 21, 22, 24, 25, 26, 28, 30, 32, 33, 35, 36, 39, 45, 65, 121.\] As part our analysis, list $N$ $J_0(N)$ (resp., $J_1(N)$, resp., $J_1(2,2N)$) has rank 0....
Article Free Access Share on Rational solutions of linear difference equations Author: Mark van Hoeij Department Mathematics, Florida State University, Tallahassee, FL FLView Profile Authors Info & Claims ISSAC '98: Proceedings the 1998 international symposium Symbolic and algebraic computationAugust Pages 120–123https://doi.org/10.1145/281508.281592Online:01 August 1998Publication History 39citation236DownloadsMetricsTotal Citations39Total Downloads236Last 12 Months11Last 6 weeks3 Get...
A new algorithm is presented for factoring bivariate approximate polynomials over C[x, y]. Given a particular polynomial, the method constructs nearby composite if one exists, and its irreducible factors. Subject to conjecture, time produce factors polynomial in degree of problem. This has been implemented Maple, demonstrated be efficient numerically robust.
We prove that van Hoeij's original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well natural variants. In particular, our approach also yields time complexity results for bivariate a finite field.
We show that almost all the linear differential operators factors obtained in analysis of n-particle contributions 's susceptibility Ising model for n ⩽ 6 are associated with elliptic curves. Beyond simplest which homomorphic to symmetric powers second order operator complete integral E, and third Z2, F2, F3, can actually be interpreted as modular forms curve model. A last order-4 globally nilpotent is not reducible this curve, form scheme. This shown correspond a natural generalization...
Article An algorithm for computing the Weierstrass normal form Share on Author: Mark van Hoeij Department of mathematics, University Nijmegen, 6525 ED The Netherlands NetherlandsView Profile Authors Info & Claims ISSAC '95: Proceedings 1995 international symposium Symbolic and algebraic computationApril Pages 90–95https://doi.org/10.1145/220346.220358Published:01 April 23citation390DownloadsMetricsTotal Citations23Total Downloads390Last 12 Months4Last 6 weeks0 Get Citation AlertsNew Alert...