AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then there are integers x1,… xs not all zero, with |F(x1,… xs)| < 1
AbstractUsing the procedure of G. I. Arkhipov and A. A. Karatsuba (Math. USSR-Izv. 19 (1982), 321–34...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
This paper is devoted to the establishment of explicit bounds on the rational function solutions of ...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135280/1/jlms0025.pd
Denote by s(r)0 the least integer such that if s⩾s(r)0 , and F is a cubic form with real coe...
AbstractLet Fx1,…,xs be a form of degree d with integer coefficients. How large must s be to ensure ...
In this thesis, we consider conditions under which certain quadratic and cubic Diophantine inequalit...
AbstractIn my paper, [Man. Math. 18 (1976), Satz 1.1] I proved a result on simultaneous diophantine ...
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which t...
AbstractLet k be an odd positive integer. Davenport and Lewis have shown that the equations a1x1k+…+...
A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points ...
AbstractThis paper obtains a result on the finiteness of the number of integer solutions to decompos...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractUsing the procedure of G. I. Arkhipov and A. A. Karatsuba (Math. USSR-Izv. 19 (1982), 321–34...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
This paper is devoted to the establishment of explicit bounds on the rational function solutions of ...
AbstractIf F is a form of odd degree k with real coefficients in s variables where s ≥ c1(k), then t...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135280/1/jlms0025.pd
Denote by s(r)0 the least integer such that if s⩾s(r)0 , and F is a cubic form with real coe...
AbstractLet Fx1,…,xs be a form of degree d with integer coefficients. How large must s be to ensure ...
In this thesis, we consider conditions under which certain quadratic and cubic Diophantine inequalit...
AbstractIn my paper, [Man. Math. 18 (1976), Satz 1.1] I proved a result on simultaneous diophantine ...
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which t...
AbstractLet k be an odd positive integer. Davenport and Lewis have shown that the equations a1x1k+…+...
A famous result due to Birch (1961) provides an asymptotic formula for the number of integer points ...
AbstractThis paper obtains a result on the finiteness of the number of integer solutions to decompos...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
AbstractIt is proved that the equation of the title has a finite number of integral solutions (x, y,...
AbstractUsing the procedure of G. I. Arkhipov and A. A. Karatsuba (Math. USSR-Izv. 19 (1982), 321–34...
We prove discrete restriction estimates for a broad class of hypersurfaces arising in seminal work o...
This paper is devoted to the establishment of explicit bounds on the rational function solutions of ...