四零点辅助函数在全部非主特征条件下估值常数的最大性之证明

Maximal evaluation constant of the assistant function with four zero points

为了更好地估计Vinogradov界,前人曾经做过2个和3个零点辅助函数的估值.该文将其推广到4个零点的情形,并证明了在全部非主特征条件下辅助函数的估值常数在全部16种情形中为最大.

To obtain a better Vinogradov's bound,predecessors construct the assistant function with two or three zero points.The assistant function with four zeros is constructed in the paper.It is also proved that the evaluation constant of the assistant function is maximal if all characters are nonprincipal character.