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On high power sums of a hybrid arithmetic function

  • Huixue Lao , Huafeng Liu and Ruotong Yu EMAIL logo
Published/Copyright: December 6, 2024
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Abstract

Let λf(n), σ(n) and ϕ(n) denote nth Fourier coefficient of the primitive holomorphic cusp form f, the sum-of-divisors function, and the Euler totient function, respectively. In this paper, we first refine related previous results on the power sum nxλfj(n)σb(n)ϕc(n) and then investigate the average behavior of the power sum n=a2+b2+c2+d2x,(a,b,c,d)Z4λfj(n)σb(n)ϕc(n).

MSC 2010: 11N37; 11F30; 11F66

Funding statement: This work is supported by the Excellent Youth Innovation Team Plan of Shandong Higher Education Institutions (Grant No. 2023KJ197), the National Natural Science Foundation of China (Grant Nos. 12171286 and 11801328) and the Natural Science Foundation of Shandong Province (Grant No. ZR2024MA053).

  1. Communicated by István Gaál

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Received: 2024-04-03
Accepted: 2024-07-01
Published Online: 2024-12-06
Published in Print: 2024-12-15

© 2024 Mathematical Institute Slovak Academy of Sciences

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