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Chowla Conjecture for the truncated Möbius function over 𝔽q[t]

  • Abhirup Chatterjee
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Abstract

In this paper we give an analytic proof of the Two-point Chowla conjecture for the truncated Möbius function μM for the function field case in the fixed q setting. We reformulate the problem into studying the distribution of (ωM,ωM∘ Ta). Thus we develop a uniform bivariate Erdős-Kac theorem in terms of the characteristic function for small pair of real numbers (u,v) via the Kubilius model. For this purpose we also develop and employ the pure Brun sieve for polynomials in this paper.

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Cite

BibTeXRIS
BibTeX
@misc{chatterjee2026chowla,
  title = {{Chowla Conjecture for the truncated Möbius function over $\mathbbF_q[t]$}},
  author = {Abhirup Chatterjee},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06471},
  eprint = {2610.06471},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06471},
}
RIS
TY  - UNPB
TI  - Chowla Conjecture for the truncated Möbius function over 𝔽_q[t]
AU  - Abhirup Chatterjee
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06471
UR  - https://arxiv.org/abs/2610.06471
AB  - In this paper we give an analytic proof of the Two-point Chowla conjecture for the truncated Möbius function μ_M for the function field case in the fixed q setting. We reformulate the problem into studying the distribution of (ω_M,ω_M∘ T_a). Thus we develop a uniform bivariate Erdős-Kac theorem in terms of the characteristic function for small pair of real numbers (u,v) via the Kubilius model. For this purpose we also develop and employ the pure Brun sieve for polynomials in this paper.
ER  -