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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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Equivalence Theorems and the Local-Global Property
TL;DR: In this article, the authors revisited some classical results about the MacWilliams equivalence theorems for codes over fields and rings, and showed that the local-global extension principle is valid for various subgroups of the group of invertible matrices.
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On Derived Equivalences of K3 Surfaces in Positive Characteristic
TL;DR: In this paper, it was shown that the Fourier-Mukai partners of an ordinary K3 surface over an algebraically closed field of positive characteristic are in one-to-one correspondence with the geometric generic fiber of its canonical lift.
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Centralizing properties in simple locally finite groups and large finite classical groups
TL;DR: In this article, it was shown that if F is an arbitrary finite subgroup of an arbitrary non-linear simple locally finite group G, then CG(F) is infinite.
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On self-similarity of $p$-adic analytic pro-$p$ groups of small dimension
Francesco Noseda,Ilir Snopce +1 more
TL;DR: In this article, the authors studied the virtual endomorphisms of a torsion-free analytic pro-$p group and showed that it admits self-similar actions on regular rooted trees.
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Some Davenport Constants with Weights and Adhikari and Rath's Conjecture.
Xingwu Xia,Zhigang Li +1 more
TL;DR: Some Davenport constants with weights are determined and the Das Adhikari and Rath conjecture that for any set A ⊆ Zn \ {0}, the equality EA(n) = DA( n) +n−1 holds is proved.