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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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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.
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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.