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A Course in Arithmetic
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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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On the transfer reducibility of certain Farrell-Hsiang groups
TL;DR: In this article, the existing proof of the Farrell-Jones Conjecture for virtually poly-mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for the validity of the conjecture.
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Counting dihedral and quaternionic extensions
TL;DR: In this article, the authors give asymptotic formulas for the number of biquadratic extensions of ℚ that admit a quadratic extension which is a Galois extension of the quaternionic group with a prescribed Galois group.
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Counting unimodular lattices in r^ r,s
TL;DR: In this paper, a new interpretation of the Gauss product of binary forms was proposed for rational Narain lattices, which brought new light to a number of related objects, such as rank 4 rational over-lattices, rank 2 primitive sublattice of an abstract rank 4 even unimodular lattice, and isomorphisms of discriminant groups of rank 2 lattices.
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Rational cubic fourfolds in Hassett divisors
Song Yang,Xun Yu +1 more
TL;DR: In this paper, it was shown that every Hassett's Noether-Lefschetz divisor of special cubic fourfolds contains a union of three codimension-two subvarieties, parametrizing rational cubic four-folds, in the moduli space of smooth cubic 4folds.
The Yang-Mills equations and the topology of 4-manifolds
TL;DR: In this paper, the authors present conditions générales d'utilisation, i.e., toute utilisation commerciale ou impression systématique is constitutive d'une infraction pénale.