منابع مشابه
Inhomogeneous Quadratic Congruences
— For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z to congruences ax+ by ≡ 0 mod q.
متن کاملQuadratic Congruences
1 Quadratic Congruences to Prime Moduli . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Quadratic Congruences to Composite Moduli . . . . . . . . . . . . . . . . . . . . . 5 3 Some Sums of Legendre’s symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 Solutions . . . . . . . . . . . . ...
متن کاملQuadratic Congruences for Cohen - Eisenstein Series
The notion of quadratic congruences was introduced in the recently appeared paper [1]. In this note we present another, somewhat more conceptual proof of several results from loc. cit. Our method allows to refine the notion and to generalize the results quoted. Here we deal only with the quadratic congruences for Cohen Eisenstein series. A similar phenomena exists for cusp forms of half-integra...
متن کاملOn almost universal ternary inhomogeneous quadratic polynomials
A fundamental question in the study of integral quadratic forms is the representation problem which asks for an effective determination of the set of integers represented by a given quadratic form. A related and equally interesting problem is the representation of integers by inhomogeneous quadratic polynomials. An inhomogeneous quadratic polynomial is a sum of a quadratic form and a linear for...
متن کاملPair Correlation Densities of Inhomogeneous Quadratic Forms
Under explicit diophantine conditions on (α, β) ∈ R2, we prove that the local two-point correlations of the sequence given by the values (m − α)2 + (n−β)2, with (m,n) ∈ Z2, are those of a Poisson process. This partly confirms a conjecture of Berry and Tabor [2] on spectral statistics of quantized integrable systems, and also establishes a particular case of the quantitative version of the Oppen...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2012
ISSN: 0208-6573
DOI: 10.7169/facm/2012.47.2.9