Results 21 to 30 of about 66 (54)
Integral points on moduli schemes of elliptic curves
Transactions of the London Mathematical Society, Volume 1, Issue 1, Page 85-115, 2014., 2014 We combine the method of Faltings (Arakelov, Paršin, Szpiro) with the Shimura–Taniyama conjecture to prove effective finiteness results for integral points on moduli schemes of elliptic curves. For several fundamental Diophantine problems, such as for example S‐unit and Mordell equations, this gives an effective method which does not rely on ...
Rafael von Känel
wiley +1 more source
Units in families of totally complex algebraic number fields
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 45, Page 2383-2400, 2004., 2004 Multidimensional continued fraction algorithms associated with GLn(ℤk), where ℤk is the ring of integers of an imaginary quadratic field K, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number fields of degrees four, six, and eight.
L. Ya. Vulakh
wiley +1 more source
Fourier Expansion‐Based Approach to the Parameter Space of Classical Systems
Annalen der Physik, Volume 538, Issue 7, July 2026.ABSTRACT We propose a new approach to compute the classical metric tensor (CMT) and the Hannay curvature using Fourier series expansions in action‐angle variables. This approach circumvents the need for complex time‐domain integrals or the construction of generating functions, replacing them with algebraic combinations of Fourier coefficients. We prove
Marcos J. Hernández +3 more
wiley +1 more source
Computing all elements of given index in sextic fields with a cubic subfield [PDF]
, 2002 summary:It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric family of number fields ...
Járási, István +5 more
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Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.Abstract Using a two‐dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non‐singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t)$\mathbb {F}_q(t)$, provided char(Fq)>3$\operatorname{char}(\mathbb {F}_q)>3$.
Jakob Glas
wiley +1 more source
Fortschritte der Physik, Volume 72, Issue 5, May 2024.Abstract The diffeomorphism class of simply connected smooth Calabi‐Yau threefolds with torsion‐free cohomology is determined via certain basic topological invariants: the Hodge numbers, the triple intersection form, and the second Chern class.
Aditi Chandra +4 more
wiley +1 more source
An algorithm for solving a certain class of Diophantine equations. I
, 1982 A class of Diophantine equations is defined and an algorithm for solving each equation in this class is developed. The methods consist of techniques for the computation of an upper bound for the absolute value of each solution. The computability of these
David Lee Hilliker
core +1 more source
The Classification of Monogenic Quartic Orders via Diophantine Equations [PDF]
In this study, we will focus on classifying quartic monogenic orders based ontwo algebraic relations. First, we introduce index forms and study the connection between the solution set of particular index form equations and the monogenizations type of ...
Shumaker, Jaxon
core +1 more source
Thue equations and related topics
, 2008 Using a classical result of Thue, we give an upper bound for the number of solutions to a family of quartic Thue equations. We also give an upper bound upon the number of solutions to a family of quartic Thue inequalities.
Akhtari, Shabnam
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Approximation Constants for Closed Subschemes of Projective Varieties [PDF]
, 2019 Diophantine approximation is a branch of number theory with a long history, going back at least to the work of Dirichlet and Liouville in the 1840s. The innocent-looking question of how well an arbitrary real algebraic number can be approximated by ...
Rollick, Nickolas
core