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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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Some New applications of General Wall Crossing Formula, Gompf’s Conjecture and its Applications
TL;DR: In this paper, the same vanishing result has been used by Taubes to show that CP 2 has a unique symplectic structure, which is the same result used by Friedman and Mrowka in proving Thom conjecture.
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On elliptic K3 surfaces.
TL;DR: A complete list of all possible ADE-types of singular fibers of complex elliptic K3 surfaces and the torsion parts of their MordellWeil groups is given in this paper.
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Superstrings from 26 dimensions
TL;DR: The finite type I superstring theories of Green and Schwarz (SO(32) and (?)E 8 × E 8 ) in ten dimensions are viewed as special dimensional reductions on 16-tori from the non-supersymmetric Veneziano-Nambu-Goto strings in 26 dimensions.
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The Dirac operator on space forms of positive curvature
TL;DR: The spectrum of the Dirac operator on spherical space forms is calculated in this paper, and a non-isometric space form with the same Dirac spectrum is constructed in the last section.