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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
Citations
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Quadratic forms and quaternion algebras: algorithms and arithmetic
John Voight,Hendrik W. Lenstra +1 more
TL;DR: In this paper, it was shown that the list of positive definite binary quadratic forms that represent the same odd primes outside of a finite set is complete outside of trivial pairs.
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What is the probability that a random integral quadratic form in n variables has an integral zero
TL;DR: In this article, it was shown that the density of quadratic forms in nn variables over ZpZp that are isotropic is a rational function of pp, where the rational function is independent of pp.
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Arithmetic intersection on a Hilbert modular surface and the Faltings height
TL;DR: In this article, an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles on a Hilbert modular surface over ρ = 0.
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Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I
Geoffrey Mason,Michael P. Tuite +1 more
TL;DR: In this article, the partition and n-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together were defined and proved holomorphic in the sewing parameters on a given suitable domain.
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Modular Ax–Lindemann–Weierstrass with Derivatives
TL;DR: An analogue of the Lindemann-Weierstrass part of Ax-Schanuel for the elliptic modular function is established to include its first and second derivatives and a generalisation is given that includes exponential and WeierstrASS elliptic functions as well.