Results 11 to 20 of about 51 (51)
Brauer–Manin obstruction for Erdős–Straus surfaces
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 746-761, August 2020., 2020 Abstract We study the failure of the integral Hasse principle and strong approximation for the Erdős–Straus conjecture using the Brauer–Manin obstruction.
Martin Bright, Daniel Loughran
wiley +1 more source
An elliptic Diophantine equation from the study of partitions [PDF]
, 2019 We present the elliptic equation X3 + 2 = Y 2 as the first in a sequence of Diophantine equations arising from some new results in the theory of partitions of multisets with equal sums.
ANDRICA, Dorin, ȚURCAȘ, George C.
core +2 more sources
How to generate all integral triangles containing a given angle
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 8, Page 569-572, 2000., 2000 We present an elementary prescription based on the rational secant method for generating all the integral triangles containing a given angle of rational cosine. This is a direct generalization of the ancient problem of finding all the Pythagorean triples. As an example, we discuss a specific equation studied by Diophantus of Alexandria, which turns out
Nelson Petulante, Ifeoma Kaja
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$E_{6}$ AND THE ARITHMETIC OF A FAMILY OF NON-HYPERELLIPTIC CURVES OF GENUS 3
Forum of Mathematics, Pi, 2015 We study the arithmetic of a family of non-hyperelliptic curves of genus 3 over the field $\mathbb{Q}$ of rational numbers. These curves are the nearby fibers of the semi-universal deformation of a simple singularity of type $E_{6}$. We show that average
JACK A. THORNE
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NON-ARCHIMEDEAN YOMDIN–GROMOV PARAMETRIZATIONS AND POINTS OF BOUNDED HEIGHT
Forum of Mathematics, Pi, 2015 We prove an analog of the Yomdin–Gromov lemma for $p$-adic definable sets and more broadly in a non-Archimedean definable context. This analog keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected ...
RAF CLUCKERS +2 more
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Complete verification of strong BSD for many modular abelian surfaces over ${\mathbf {Q}}$
Forum of Mathematics, SigmaWe develop the theory and algorithms necessary to be able to verify the strong Birch–Swinnerton-Dyer Conjecture for absolutely simple modular abelian varieties over ${\mathbf {Q}}$ . We apply our methods to all 28 Atkin–Lehner quotients of $X_0(
Timo Keller, Michael Stoll
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Preliminary characterization and localization of three candidate biomineralization proteins in Emiliania huxleyi [PDF]
, 2014 The marine phytoplankton, E. huxleyi, synthesizes calcite disks in an intracellular golgi-derived complex known as the coccolith vesicle. Synthesis is thought to involve the coordinated activity of a polysaccharide-protein polymer complex that acts both ...
Wesley Erik Shipley
core
Rational torsion points on abelian surfaces with quaternionic multiplication
Forum of Mathematics, SigmaLet A be an abelian surface over ${\mathbb {Q}}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur’s theorem for elliptic curves, we show that the torsion subgroup of $A({\mathbb {Q}})$
Jef Laga +3 more
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The genus of curves over finite fields with many rational points, [PDF]
, 1996 . We prove the following result which was conjectured by Stichtenoth and Xing: let g be the genus of a projective, non-singular, geometrically irreducible, algebraic curve defined over the finite field with q 2 elements whose number of rational points ...
Rainer Fuhrmann, Fernando Torres
core
Rank jumps and multisections of elliptic fibrations on K3 surfaces
Forum of Mathematics, SigmaWe consider the countably many families $\mathcal {L}_d$ , $d\in \mathbb {N}_{\geq 2}$ , of K3 surfaces admitting an elliptic fibration with positive Mordell–Weil rank. We prove that the elliptic fibrations on the very general member of these
Alice Garbagnati, Cecília Salgado
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