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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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Basic quadratic forms
TL;DR: A brief classical introduction Quadratic spaces and lattices Valuations, local fields, and $p$-adic numbers Quadralatic spaces over $\mathbb{Q}_p$ Quadralastic spaces over \mathbb {Q}$ Lattices over principal ideal domains Initial integral results Local classification of lattices The local-global approach to lattices Lattice over \mb{F}_q[x]$ Applications to cryptography Further reading Bibliography Index.
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Bounds for Rankin-Selberg integrals and quantum unique ergodicity for powerful levels
TL;DR: In this paper, the authors presented a method for the detection of cancer using the Web of Science Record created on 2014-10-23, modified on 2017-12-10.
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Supersymmetry and the Mobius Inversion Function
TL;DR: In this article, it was shown that the Mobius inversion function of number theory can be interpreted as the operator (−1)F in quantum field theory, which is equivalent to the prime number theorem.
Journal Article
Moduli stacks of polarized K3 surfaces in mixed characteristic
TL;DR: In this paper, the moduli functors of K3 spaces with a primitive polarization of degree 2d and a level structure are represented by smooth algebraic spaces over open parts of Spec(Z).