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A Course in Arithmetic
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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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Anomalies, characters and strings
TL;DR: One-loop modular invariant heterotic and type II closed string theories are proved to be anomaly free, apart from terms proportional to Tr F 2 − Tr R 2, and it is shown why this conclusion holds with remarkable generality for any conceivable fermionic string theory, regardless even of conformal invariance.
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Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks
TL;DR: In this article, the first examples of K3 surface automorphisms with Siegel disks are presented, and the set of such examples is countable, and a surface must be non-projective to carry a Siegel disk.
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Toroidal compactification of non-supersymmetric heterotic strings
Paul Ginsparg,Cumrun Vafa +1 more
TL;DR: In this paper, it was shown that all the recently discovered rank-16 non-supersymmetric heterotic strings form a single connected class of theories when compactified on tori in the presence of constant background fields.