Systems of quadratic diophantine inequalities
نویسنده
چکیده
has a nonzero integer solution for every > 0. If some Qi is rational and is small enough then for x ∈ Zs the inequality |Qi(x)| < is equivalent to the equation Qi(x) = 0. Hence if all forms are rational then for sufficiently small the system (1.1) reduces to a system of equations. In this case W. Schmidt [10] proved the following result. Recall that the real pencil generated by the forms Q1, . . . , Qr is defined as the set of all forms
منابع مشابه
Some Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables
In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. In particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.
متن کاملA Solvable Class of Quadratic Diophantine Equations with Applications to Verification of Infinite-State Systems
A -system consists of quadratic Diophantine equations over nonnegative integer variables of the form:
متن کاملQuadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces
In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right)right|, nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|
متن کاملOld and New Conjectured Diophantine Inequalities
The original meaning of diophantine problems is to find all solutions of equations in integers or rational numbers, and to give a bound for these solutions. One may expand the domain of coefficients and solutions to include algebraic integers, algebraic numbers, polynomials, rational functions, or algebraic functions. In the case of polynomial solutions, one tries to bound their degrees. Inequa...
متن کامل