ISSN:
1570-5846
Keywords:
binary forms
;
representation problems
;
higher degree equations
;
Diophantine approximation
;
Waring's problem and variants
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let a, b and n be integers with ≥ 3. We show that, in the sense of natural density, almost all integers represented by the binary form axn − byn are thus represented essentially uniquely. By exploiting this conclusion, we derive an asymptotic formula for the total number of integers represented by such a form. These conclusions augment earlier work of Hooley concerning binary cubic and quartic forms, and generalise or sharpen work of Hooley, Greaves, and Skinner and Wooley concerning sums and differences of two nth powers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1000270823971
Permalink
