منابع مشابه
Real Quadratic Double Sums
In 1988, Andrews, Dyson and Hickerson initiated the study of q-hypergeometric series whose coefficients are dictated by the arithmetic in real quadratic fields. In this paper, we provide a dozen q-hypergeometric double sums which are generating functions for the number of ideals of a given norm in rings of integers of real quadratic fields and prove some related identities.
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We investigate the asymptotic distribution of integrals of the j-function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asymptotic formula, we prove a bound for sums of Kloosterman sums of half-integral weight which is uniform in every parameter. To establish this estimate we prove a variant of Kuznetsov’s formula where the spectral data is re...
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The most powerful methods for handling these sums exploit the modern theory of automorphic forms; see [DFI1] for spectral aspects and [DIT] for more arithmetical connections. The sum (1.1) has only a few terms, bounded by the divisor function, so there is not much room for cancellation, but for applications there is a lot of interest in bounds for sums of these as the modulus c varies, say (1.2...
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It is a well-known problem to give an estimate for the largest clique of the Paley-graph, i.e. , to give an estimate for |A| if A ⊂ Fp (p ≡ 1 (mod 4)) is such that A−A = {a−a′ |a, a′ ∈ A} avoids the set of quadratic nonresidues. In this paper we will study a much simpler problem namely when A− A is substituted by the set FS(A) = { ∑ εaa | εa = 0 or 1 and ∑ εa > 0}. In other words we will estima...
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Let p be an odd prime and {χ(m) = (m/p)}, m = 0,1, . . . ,p − 1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ modp which are defined in terms of the Legendre symbol (m/p), (m,p)= 1. We study the relation between the Gauss and the quadratic Gauss sums. It is shown that the quadratic Gauss sumsG(k;p) are equal to the Gauss sums G(k,χ) that correspond to this ...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2015
ISSN: 0019-3577
DOI: 10.1016/j.indag.2015.06.002