We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.
|Number of pages||17|
|Journal||Canadian Journal of Mathematics . Journal Canadien de Mathematiques|
|Publication status||Published - Feb 2011|
- exponential sums
- Diophantine equations
- WARING PROBLEM