Results 21 to 30 of about 1,078 (72)
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
The Method Of Thue-Siegel For Binary Quartic Forms
, 2009 We will use Thue-Siegel method, based on Pad\'e approximation via hypergeometric functions, to give upper bounds for the number of integral solutions to the equation $|F(x, y)| = 1$ as well as the inequalities $|F(x, y)| \leq h$, for a certain family of ...
Akhtari, Shabnam
core +1 more source
Elliptic Curves and Hyperdeterminants in Quantum Gravity [PDF]
, 2010 Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely ignored over a period of 100 years before once again being recognised as ...
Gibbs, Philip
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On the simplest sextic fields and related Thue equations [PDF]
, 2010 We consider the parametric family of sextic Thue equations \[ x^6-2mx^5y-5(m+3)x^4y^2-20x^3y^3+5mx^2y^4+2(m+3)xy^5+y^6=\lambda \] where $m\in\mathbb{Z}$ is an integer and $\lambda$ is a divisor of $27(m^2+3m+9)$.
Hoshi, Akinari
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A note on Diophantine systems involving three symmetric polynomials
, 2013 Let $\bar{X}_{n}=(x_{1},\ldots,x_{n})$ and $\sigma_{i}(\bar{X}_{n})=\sum x_{k_{1}}\ldots x_{k_{i}}$ be $i$-th elementary symmetric polynomial. In this note we prove that there are infinitely many triples of integers $a, b, c$ such that for each $1\leq i ...
Ulas, Maciej
core +1 more source
Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations [PDF]
, 2015 We establish the non-singular Hasse principle for systems of three diagonal quartic equations in 32 or more variables, subject to a certain rank condition.
Bruedern, Joerg, Wooley, Trevor D.
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What is Mathematics and What Should it Be
, 2017 This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.Comment: 10 ...
Zeilberger, Doron
core +1 more source
Quartic Forms in Many Variables [PDF]
, 2014 We show that a quartic $p$-adic form with at least $3192$ variables possesses a non-trivial zero. We also prove new results on systems of cubic, quadratic and linear forms.
Dumke, Jan H.
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Perspectives on mathematics competitions and their relationship with mathematics education. [PDF]
ZDM, 2022 de Losada MF, Taylor PJ.
europepmc +1 more source
The Manin conjecture in dimension 2
, 2007 These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.Comment: 57 pages. These are a preliminary version of lecture notes for the "School and conference on analytic number theory", ICTP ...
Browning, T. D.
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