The inhomogeneous minimum of a ternary quadratic form (II)
نویسندگان
چکیده
منابع مشابه
Ramanujan’s Ternary Quadratic Form
do not seem to obey any simple law.” Following I. Kaplansky, we call a non-negative integer N eligible for a ternary form f(x, y, z) if there are no congruence conditions prohibiting f from representing N. By the classical theory of quadratic forms, it is well known that any given genus of positive definite ternary quadratic forms represents every eligible integer. Consequently if a genus consi...
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This paper proves that if N is a nonnegative eligible integer, coprime to 7, which is not of the form x2+y2+7z2, thenN is square-free. The proof is modelled on that of a similar theorem by Ono and Soundararajan, in which relations between the number of representations of an integer np2 by two quadratic forms in the same genus, the pth coefficient of an L-function of a suitable elliptic curve, a...
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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...
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Ramanujans Ternary Quadratic Form represents a series of numbers that satisfy a tripartite quadratic relation. In the present work, we examine the sequence of numbers generated by such forms and other related forms obtained by varying the coefficients and exponents to other values. Chaotic characterization using standard techniques such as Lyapunov Exponents, Kolmogorov Entropy, Fractal Dimensi...
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Abstract. Denote by ‖ · ‖ the euclidean norm in R. We prove that the local pair correlation density of the sequence ‖m− α‖k, m ∈ Z, is that of a Poisson process, under diophantine conditions on the fixed vector α ∈ R: in dimension two, vectors α of any diophantine type are admissible; in higher dimensions (k > 2), Poisson statistics are only observed for diophantine vectors of type κ < (k − 1)/...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1956
ISSN: 0001-5962
DOI: 10.1007/bf02392358