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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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Applications of Kronecker’s limit formula for elliptic Eisenstein series
TL;DR: In this paper, the Kronecker limit function associated to certain elliptic fixed points for a few small level moonshine groups has been derived, specifically for congruence subgroups and non-compact subgroups with one cusp.
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Lattice vertex algebras on general even, self-dual lattices
TL;DR: In this paper, the authors analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices with p ≥ q and show that the resulting non-GKM Lie algebra cannot be described conveniently in terms of generators and relations.
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On the zeros of certain modular functions for the normalizers of congruence subgroups of low levels II
TL;DR: In this article, the location of the zeros of the Eisenstein series and the modular functions from the Hecke type Faber polynomials associated with the normalizers of congruence subgroups which are of genus zero and of level at most twelve were investigated.
Lectures on Multiple Zeta Values IMSC 2011
TL;DR: It is known that π is a transcendental number the authors, and that all ζ(2n, n ≥ 1) is irrational (see, e.g., the authors ).