Let m0,m1,m2,…be positive integers with mi〉 2 for all i. It is well known that each nonnegative integer n can be uniquely represented as n= a0 + a1m0+a2m0m1+…+atm0m1m2…mt-1,where 0≤ai≤mi-1 for all i and at≠...Let m0,m1,m2,…be positive integers with mi〉 2 for all i. It is well known that each nonnegative integer n can be uniquely represented as n= a0 + a1m0+a2m0m1+…+atm0m1m2…mt-1,where 0≤ai≤mi-1 for all i and at≠0.let each fi be a function defined on {0,1,2…,mi-1} with fi(0)=0.write S(n)=i=0∑tfi(ai).In this paper, we give the asymptotic formula for x^-1∑n≤xS(n)^k,where k is a positive integer.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10771103)
文摘Let m0,m1,m2,…be positive integers with mi〉 2 for all i. It is well known that each nonnegative integer n can be uniquely represented as n= a0 + a1m0+a2m0m1+…+atm0m1m2…mt-1,where 0≤ai≤mi-1 for all i and at≠0.let each fi be a function defined on {0,1,2…,mi-1} with fi(0)=0.write S(n)=i=0∑tfi(ai).In this paper, we give the asymptotic formula for x^-1∑n≤xS(n)^k,where k is a positive integer.