English

Finite Ramanujan expansions and shifted convolution sums of arithmetical functions

Number Theory 2016-12-12 v1

Abstract

For two arithmetical functions ff and gg, we study the convolution sum of the form nNf(n)g(n+h)\sum_{n \le N} f(n) g(n+h) in the context of its asymptotic formula with explicit error terms. Here we introduce the concept of finite Ramanujan expansion of an arithmetical function and extend our earlier works in this setup.

Keywords

Cite

@article{arxiv.1612.03136,
  title  = {Finite Ramanujan expansions and shifted convolution sums of arithmetical functions},
  author = {Giovanni Coppola and M. Ram Murty and Biswajyoti Saha},
  journal= {arXiv preprint arXiv:1612.03136},
  year   = {2016}
}