关于二项指数和的均值

On Mean Values of Two-Term Exponential Sums

针对著名的Smararadche问题,有很多有趣的均值及相应的渐近公式,利用这些函数的均值及渐进公式可以为工程或其它方面的需要进行估值,指数和的均值计算是其中很重要的问题之一.尤其是近年来,人们引入了二项指数和,给出了一些特殊情况下二项指数和复合后函数的均值.推广了这些结果,给出了二项指数和C(m,n,h,k;q)关于正整数q的一个递归公式,以及q=pα(α≥1)时某些特定条件下C(m,n,h,k;q)的均值,其中p为奇素数.

It is well known that there are many interesting mean values and asymptotic formulae of some arithmetic functions related to the Smararadch problem,which has applications in engineering field.In these investigations,the mean value for exponential sums is very important.In recent years,the two-term exponential sum is introduced and the computing formula is given in some cases.The present paper generalizes their results and a recursive formula for computing the two-term exponential sum C （m,n,h,k;q） is given,where q is a positive integer.In particular,when q is a power of the odd prime number p,the mean value for C（m,n,h,k;q） is obtained in some cases.