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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.

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Book ChapterDOI

Extension Theorems for Linear Codes over Finite Rings

TL;DR: The Extension theorem for symmetrized weight compositions over finite Frobenius rings is proved and an extension theorem for weight functions over certain finite commutative rings is also proved.
Posted Content

The Hodge-de~Rham Theory of Modular Groups

TL;DR: In this paper, the authors give a context to Manin's iterated Shimura integrals (iterated integrals of modular forms) and study relations in the "maximal Eisenstein quotient" of the completion of SL_2(Z).
Book ChapterDOI

Undecidability in Number Theory

TL;DR: In this paper, the authors give sketches of classical undecidability results in number theory, like Godel's first Incompleteness Theorem (that the first order theory of the integers in the language of rings is undecidable), Julia Robinson's extensions of this result to arbitrary number fields and rings of integers in them, as well as to the ring of totally real integers.
Journal ArticleDOI

Self-maps of projective spaces

TL;DR: In this article, the authors considered the problem of classifying self maps of iterated suspensions of real, complex, and quaternionic projective spaces, up to homology.
Journal ArticleDOI

Heights of kudla-rapoport divisors and derivatives of l-functions

TL;DR: In this article, the authors constructed an arithmetic theta lift from harmonic Maass forms of weight 2 n to the arithmetic Chow group of the integral model of a unitary Shimura variety associated with unitary similitude groups of signature (n-1, 1, 1) by associating to a linear combination of Kudla-Rapoport divisors.