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A Course in Arithmetic
TLDR
In this article, the theorem on arithmetic progressions modular forms is proved for finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratics forms with discriminant +-1.Abstract:
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.read more
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Automorphisms and Periods of Cubic Fourfolds
Radu Laza,Zhiwei Zheng +1 more
TL;DR: In this paper, the Torelli theorem for cubic four-folds and the classification of the fixed-point sublattices of the Leech lattice were used to classify the symplectic automorphism groups for cubic 4-fold automorphisms.
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Parameterizing N-Holed Tori
Cindy Grimm,John Hughes +1 more
TL;DR: A parameterization for an n-holed tori based on the hyperbolic polygon is defined and the domain is model using a manifold with 2n+2 charts, and linear fractional transformations for transition functions.
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Modular forms and $k$-colored generalized Frobenius partitions
TL;DR: In this article, the authors studied the modular forms of positive integers using the theory of modular forms and discovered new surprising properties of the generating function of the generalized Frobenius partitions.
Journal ArticleDOI
On polynomial-factorial diophantine equations
Daniel Berend,Jørgen E. Harmse +1 more
TL;DR: In this article, it was shown that for some classes of polynomials P the equation x r (x + 1) = n! has only finitely many solutions for r > 4, but not that this is the case for r < 3.
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Isodual constacyclic codes
TL;DR: This paper determines the constacyclic codes over F q (of length prime to q) that are isometric to their dual via a multiplier through a multiplier.