JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 70-74.doi: 10.6040/j.issn.1671-9352.0.2016.505

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On the mean value of a hybrid arithmetic function

LI Ting-ting, LAO Hui-xue*   

  1. School of Mathematics and Statistics, ShanDong Normal University, Jinan 250014, Shandong, China
  • Received:2016-10-31 Online:2017-08-20 Published:2017-08-03

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Abstract: Let λf(n) be the Fourier coefficients of cusp forms of the normalized Hecke operator Tn, σ(n) be the sum-of-divisors function, and φ(n) be the Eulers function. The average order estimation of hybrid arithmetic functions of the form λf(n)σb(n)φc(n) is investigated by using analytic methods, and the upper bound estimate ∑n≤xλf(n)σb(n)φc(n)≪xb+c+1/2+ε,for any ε>0 is obtained.

Key words: holomorphic cusp form, Fourier coefficients, automorphic L-function, arithmetic function

CLC Number: 

  • O157.5
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