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A Course in Arithmetic
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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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Phase transitions on Hecke C*-algebras and class-field theory over ℚ
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Distance and tube zeta functions of fractals and arbitrary compact sets
TL;DR: In this article, it was shown that the abscissa of absolute convergence of ζ A is equal to dim B A, the upper box (or Minkowski) dimension of A, under some mild conditions.
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Local diophantine properties of modular curves of -elliptic sheaves
TL;DR: In this article, the existence of rational points on modular curves of ǫ-elliptic sheaves over local fields and the structure of special fibres of these curves were studied.