Denote by s(r)0 the least integer such that if s⩾s(r)0 , and F is a cubic form with real coefficients in s variables that splits into r parts, then F takes arbitrarily small values at nonzero integral points. We bound s(r)0 for r⩽6
We discuss small solutions to ternary diagonal inequalities of any degree where all of the variables...
A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four...
We will give new upper bounds for the number of solutions to the inequalities of the shape |F(x, y)|...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135280/1/jlms0025.pd
In this thesis, we consider conditions under which certain quadratic and cubic Diophantine inequalit...
1. Let f (x1, x2, ..., xn) be a homogeneous form with real coefficients in n variables x1, x2, ..., ...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
Let C be a cubic form with integer coefficients in n variables, and let h be the h-invariant of C. L...
We consider a system of R cubic forms in n variables, with integer coefficients, which define a smoo...
In this article we establish two new results on quantitative Diophantine approximation for one-param...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
Let $S$ be a finite set of primes. The $S$-part $[m]_S$ of a non-zero integer $m$ is the largest pos...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
AbstractFor an indefinite quadratic form f(x1, …, xn) let P(f) denote the greatest lower bound of th...
AbstractFor homogeneous decomposable forms F(X) in n variables with real coefficients, we consider t...
We discuss small solutions to ternary diagonal inequalities of any degree where all of the variables...
A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four...
We will give new upper bounds for the number of solutions to the inequalities of the shape |F(x, y)|...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135280/1/jlms0025.pd
In this thesis, we consider conditions under which certain quadratic and cubic Diophantine inequalit...
1. Let f (x1, x2, ..., xn) be a homogeneous form with real coefficients in n variables x1, x2, ..., ...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
Let C be a cubic form with integer coefficients in n variables, and let h be the h-invariant of C. L...
We consider a system of R cubic forms in n variables, with integer coefficients, which define a smoo...
In this article we establish two new results on quantitative Diophantine approximation for one-param...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
Let $S$ be a finite set of primes. The $S$-part $[m]_S$ of a non-zero integer $m$ is the largest pos...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
AbstractFor an indefinite quadratic form f(x1, …, xn) let P(f) denote the greatest lower bound of th...
AbstractFor homogeneous decomposable forms F(X) in n variables with real coefficients, we consider t...
We discuss small solutions to ternary diagonal inequalities of any degree where all of the variables...
A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four...
We will give new upper bounds for the number of solutions to the inequalities of the shape |F(x, y)|...
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