Averages of shifted convolution sums for arithmetic functions  

作　　者：Miao LOU 

机构地区：[1]School of Mathematics, Shandong University, Jinan 250100, China

出　　处：《Frontiers of Mathematics in China》2019年第1期123-134,共12页中国高等学校学术文摘·数学（英文）

摘　　要：Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolution sums of the type Σ|h|≤H |ΣX<n≤2XAf (1,…, 1, n+h)λ(n)|^2. We succeed in obtaining a saving of an arbitrary power of the logarithm, provided that X^8/33+ε≤H≤X^1-ε.

关 键 词：AVERAGE shifted CONVOLUTION SUM ARITHMETIC function 

分 类 号：O[理学]