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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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Equivariant Euler characteristics of partition posets
TL;DR: All the equivariant Euler characteristics of the $\Sigma_n$-poset of partitions of partition of the $n$ element set are computed.
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Bootstrapping ADE M-strings
Zhihao Duan,June Nahmgoong +1 more
TL;DR: In this paper, a kinematical constraint that elliptic genera of ADE-type M-strings in 6d (2.0) SCFTs should follow the Gopakumar-Vafa invariants was proposed.
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Nearly unimodular quadartic forms
TL;DR: In this paper, it was shown that every unimodular 2-lattice occurs as a homology group of a simply connected, closed, topological 4-manifold if and only if they have the same rank, type, and signature.
Posted Content
Generating spaces of modular forms with $\eta$-quotients
TL;DR: In this article, the authors consider a question of Ono concerning which spaces of classical modular forms can be generated by sums of sums of $\eta$-quotients, and give some new examples of spaces of modular forms which can be created as sums of ∆-quantity quotients.
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The smallest hyperbolic 6-manifolds
TL;DR: In this article, the first known hyperbolic 6-manifolds with Euler characteristic -1 were constructed by gluing together copies of an all-right- angled Coxeter polytope.