Pairs of Additive Congruences to a Large Prime Modulus Original Research Article

It is known that a system of two additive equations of degreekwith greater than 4kvariables has a non-trivialp-adic solution for allp>k6. The purpose of this paper is to improve this result top>3k4. A considerable modification of the standard method of exponential sums is introduced which uses the Hasse–Weil sum estimate for multiplicative characters.