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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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Lattices with theta functions for G(√2) and linear codes
TL;DR: In this article, a modular hermitian lattice with an extremal theta-function was constructed in C 2n for all n R 4n for n = 1, 4, and 8.
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CM values of regularized theta lifts and harmonic weak Maaß forms of weight 1
TL;DR: In this article, it was shown that regularized theta lifts at complex multiplication points can be expressed in terms of finitely many Fourier coefficients of certain harmonic weak Maafi forms of weight 1, whose prime ideal factorization is determined by special cycles on an arithmetic curve.
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Chiral gravity in two-dimensions
Robert C. Myers,Vipul Periwal +1 more
TL;DR: In this article, it is shown that conformal matter with cL ≠ cR can be consistently coupled to two-dimensional "frame" gravity, and a non-critical heterotic string is constructed.
Journal Article
Symmetries of order four on K3 surfaces
TL;DR: In this paper, a classification of purely non-symplectic automorphisms by relating the structure of their fixed locus to their action on cohomology is given, in the following cases: the fixed locality contains a curve of genus g>0; the fixed locuse contains at least a curve; all the curves fixed by the square of the automorphism are rational; and partial results in other cases are given.