Displaying similar documents to “Pairs of additive quadratic forms modulo one”

The circle method and pairs of quadratic forms

Henryk Iwaniec, Ritabrata Munshi (2010)

Journal de Théorie des Nombres de Bordeaux

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We give non-trivial upper bounds for the number of integral solutions, of given size, of a system of two quadratic form equations in five variables.

CM liftings of supersingular elliptic curves

Ben Kane (2009)

Journal de Théorie des Nombres de Bordeaux

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Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D < 0 such that the reduction map modulo a prime above p from elliptic curves with CM by 𝒪 D to supersingular elliptic curves in characteristic p is surjective. In the algorithm we first determine an explicit constant D p so that | D | > D p implies that the map is necessarily surjective and then we compute explicitly the cases | D | < D p .

A characterization of some additive arithmetical functions, III

Jean-Loup Mauclaire (1999)

Acta Arithmetica

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I. Introduction. In 1946, P. Erdős [2] proved that if a real-valued additive arithmetical function f satisfies the condition: f(n+1) - f(n) → 0, n → ∞, then there exists a constant C such that f(n) = C log n for all n in ℕ*. Later, I. Kátai [3,4] was led to conjecture that it was possible to determine additive arithmetical functions f and g satisfying the condition: there exist a real number l, a, c in ℕ*, and integers b, d such that f(an+b) - g(cn+d) → l, n → ∞. This problem...

Five regular or nearly-regular ternary quadratic forms

William C. Jagy (1996)

Acta Arithmetica

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1. Introduction. In a recent article [6], the positive definite ternary quadratic forms that can possibly represent all odd positive integers were found. There are only twenty-three such forms (up to equivalence). Of these, the first nineteen were proven to represent all odd numbers. The next four are listed as "candidates". The aim of the present paper is to show that one of the candidate forms h = x² + 3y² + 11z² + xy + 7yz does represent all odd (positive) integers, and that it is...

Primitive minima of positive definite quadratic forms

Aloys Krieg (1993)

Acta Arithmetica

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The main purpose of the reduction theory is to construct a fundamental domain of the unimodular group acting discontinuously on the space of positive definite quadratic forms. This fundamental domain is for example used in the theory of automorphic forms for GLₙ (cf. [11]) or in the theory of Siegel modular forms (cf. [1], [4]). There are several ways of reduction, which are usually based on various minima of the quadratic form, e.g. the Korkin-Zolotarev method (cf. [10], [3]),...

Singular quadratic functionals of one dependent variable

Zuzana Došlá, Ondřej Došlý (1995)

Commentationes Mathematicae Universitatis Carolinae

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Singular quadratic functionals of one dependent variable with nonseparated boundary conditions are investigated. Necessary and sufficient conditions for nonnegativity of these functionals are derived using the concept of and . The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.