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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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Equivariant Euler characteristics of subspace posets
TL;DR: In this article, the (p-primary) equivariant reduced Euler characteristics of the building for the general linear group over a finite field were determined, where p is the p-primary Euler constant.
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Dynkin diagrams of rank 20 on supersingular K 3 surfaces
Ichiro Shimada,De-Qi Zhang +1 more
TL;DR: In this article, the authors classify normal supersingular K3 surfaces with total Milnor number 20 in characteristic p, where p is an odd prime that does not divide the discriminant of the Dynkin type of the rational double points on Y.
Journal Article
Class numbers of orders in quartic fields
TL;DR: In this article, it was shown that the sum of class numbers of orders in totally complex quartic fields with no real quadratic subfield obeys an asymptotic law similar to the prime numbers, as the bound on the regulators tends to infinity.
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Lattice classification of the eight-dimensional chiral heterotic strings
TL;DR: In this paper, the eight-dimensional chiral rank-18 heterotic strings were classified using the covariant lattice approach, and the results showed that the lattice-based approach is more robust than the traditional lattice based approach.
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A reduction point algorithm for cocompact Fuchsian groups and applications
Pilar Bayer,Dionís Remón +1 more
TL;DR: A reduction point algorithm is proposed for any Fuchsian group in the absence of parabolic transformations, such as the flip flop algorithm known for the modular group $\mathbf{SL}(2, \mathbb{Z})$ and whose roots go back to [9].