Results 11 to 20 of about 69 (56)
Quartic Index Form Equations and Monogenizations of Quartic Orders
, 2022 Some upper bounds for the number of monogenizations of quartic orders are established by considering certain classical Diophantine equations, namely index form equations in quartic number fields, and cubic and quartic Thue equations.Comment: a version of
Akhtari, Shabnam
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, 2021 Talking about the Diophantine analysis’ history, namely, the problem of rational solutions of Diophantine equations, we should note the longevity of the algebraic approach, which goes back to Diophantus’ “Arithmetica”.
Беляев А.А. +3 more
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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
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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
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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
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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
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Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields [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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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
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Introductory Algebraic Number Theory [PDF]
, 2003 If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational
Julio Pérez-Hernández +5 more
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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
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