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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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Dimension formula for graded Lie algebras and its applications
Seok-Jin Kang,Myung-Hwan Kim +1 more
TL;DR: In this paper, the Euler-Poincare principle yields the denominator identities for the Γ-graded Lie algebras, from which a dimension formula for the homogeneous subspaces Lα (α ∈ Γ) is derived.
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Codes over GF(4) and complex lattices
TL;DR: The theta-functions of self-dual lattices are characterized and two general methods for constructing lattices from codes are presented, including a new lattice sphere-packing in R 36.
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On ad-semisimple Lie algebras
TL;DR: In this paper, the Brauer group of the underlying field and the isomorphism classes of simple-semi-belabelian Lie algebras are studied, and it is shown that the relation between these classes and the Lie algebra ad-semisimple problem is not a straightforward one.
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Donaldson-Witten theory and indefinite theta functions
Georgios Korpas,Jan Manschot +1 more
TL;DR: In this article, the authors considered partition functions with insertions of surface operators of topologically twisted SU(2) supersymmetric Yang-Mills theory on a four-manifold.
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Prime numbers and the first digit phenomenon
Daniel I.A Cohen,Talbot M. Katz +1 more
TL;DR: In this paper, it was shown that for any generalization of relative natural density (obeying a few basic assumptions) if a value is assigned to the relative density of primes of lead digit 1 then this value is always log 10 2.