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On Ramanujan-Fourier expansions

Number Theory 2023-05-30 v1
Authors: David T. Nguyen
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Abstract

We heuristically study the shifted convolution ∑n≤Xτk(n)τℓ(n+h)\sum_{n\le X} \tau_k(n) \tau_\ell(n+h) using a normalized version of Ramanujan-Fourier expansions for τk(n)\tau_k(n) and verify they produce the expected answer.

Cite

@article{arxiv.2305.17597,
  title  = {On Ramanujan-Fourier expansions},
  author = {David T. Nguyen},
  journal= {arXiv preprint arXiv:2305.17597},
  year   = {2023}
}

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six pages

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