Results 21 to 30 of about 56 (52)
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
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
Integral zeroes of Krawtchouk polynomials [PDF]
, 2012 This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.Krawtchouk polynomials appear in many various areas of mathematics starting from discrete mathematics (e.g., in coding theory), association schemes, and in ...
Alenezi, Ahmad M
core
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
От алгебраических методов Диофанта - Ферма - Эйлера к арифметике алгебраических кривых: из истории диофантовых уравнений после Эйлера [PDF]
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. +1 more
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Thue equations and related topics [PDF]
, 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
core
Indices dans les corps de nombres et leurs applications [PDF]
, 2018 Dans la première partie de cette thèse, on considère les extensions cycliques simples Km/Q de degré 4. Ces dernières sont les extensions quartiques définies par les polynômes irréductibles x⁴-mx³-6x²+mx+1, où m est un entier tel que la partie impaire ...
Seddik, Mohammed
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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
Computing all integer solutions of a genus 1 equation [PDF]
The Elliptic Logarithm Method has been applied with great successto the problem of computing all integer solutions of equations ofdegree 3 and 4 defining elliptic curves. We extend this methodto include any equation f(u,v)=0 that defines a curve of genus
Stroeker, R.J., Tzanakis, N.
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