Open AccessBook
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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Journal ArticleDOI
On the sign changes of coefficients of general Dirichlet series
TL;DR: In this paper, the authors invoked Laguerre's Rule of Signs and Landau's Theorem to provide a simple answer to the question under what conditions do the coefficients of a general Dirichlet series exhibit oscillatory behavior.
Journal ArticleDOI
On the image of the -adic Abel-Jacobi map for a variety over the algebraic closure of a finite field
TL;DR: In this article, the Tate conjecture is shown to be surjective when the Abel-Jacobi map of a smooth projective k0-variety is constructed by a non-negative function.
Journal ArticleDOI
Unirationality of certain supersingular K3 surfaces in characteristic 5
Duc Tai Pho,Ichiro Shimada +1 more
TL;DR: In this article, it was shown that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational, and that any surface with artin invariance ≥ 3 is also unirherent.
Journal ArticleDOI
Toy models for D. H. Lehmer's conjecture
Eiichi Bannai,Tsuyoshi Miezaki +1 more
TL;DR: In this article, it was shown that the m-th Fourier coefficient of the weighted theta series of the A 2-lattice does not vanish when the shell of norm m of those lattices is not the empty set.
Book ChapterDOI
Some Eisenstein Series Identities Associated with the Borwein Functions
TL;DR: In this paper, the Borweins' cubic theta function identity and Jacobi's Jacobi identity were derived from a well-known identity involving theta-functions and one identity of Ramanujan.