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A Course in Arithmetic
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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Vector bundles over a nondegenerate conic
Indranil Biswas,D. S. Nagaraj +1 more
TL;DR: In this paper, the authors classify all the isomorphism classes of vector bundles over the projective line in the k-form of a field and X a k-formation of the line.
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The two-prime analogue of the Hecke C*-algebra of Bost and Connes
TL;DR: In this paper, a semigroup crossed product C * (G p,q ) x α N 2 is analyzed, and the structure of one of the subquotients reflects interesting number-theoretic information about multiplicative orders of q in the rings Z/p Z.
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Stable Cohomotopy Seiberg-Witten Invariants of Connected Sums of Four-Manifolds with Positive First Betti Number
Masashi Ishida,Hirofumi Sasahira +1 more
TL;DR: The non-vanishing theorem for the stable cohomotopy Seiberg-Witten invariant of connected sums of 4-manifolds with positive first Betti number was proved in this article.
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Half-integral weight modular forms and real quadratic $p$-rational fields
Jilali Assim,Zakariae Bouazzaoui +1 more
TL;DR: In this paper, a criterion for the existence of real quadratic $p$-rational fields is given. But this criterion is not applicable to the case of real-valued rational fields.
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Fake projective planes
Gopal Prasad,Sai-Kee Yeung +1 more
TL;DR: In this paper, Mumford et al. used the arithmeticity of the fundamental group of fake projective planes, the formula for the covolume of principal arithmetic subgroups given by the first-named auhor, and some number theoretic estimates.