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Mathematics > Number Theory

arXiv:1803.08140 (math)
[Submitted on 21 Mar 2018 (v1), last revised 6 Sep 2018 (this version, v2)]

Title:On locally repeated values of arithmetic functions over $\mathbb F_q[T]$

Authors:Ze'ev Rudnick
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Abstract:The frequency of occurrence of "locally repeated" values of arithmetic functions is a common theme in analytic number theory, for instance in the Erdős-Mirsky problem on coincidences of the divisor function at consecutive integers, the analogous problem for the Euler totient function, and the quantitative conjectures of Erdős, Pomerance and Sarkőzy and of Graham, Holt and Pomerance on the frequency of occurrences. In this paper we introduce the corresponding problems in the setting of polynomials over a finite field, and completely solve them in the large finite field limit.
Comments: with an Appendix by Ron Peled. Minor revision. Accepted for publication in the Quarterly Journal of Math
Subjects: Number Theory (math.NT); Probability (math.PR)
Cite as: arXiv:1803.08140 [math.NT]
  (or arXiv:1803.08140v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1803.08140

Submission history

From: Zeev Rudnick [view email]
[v1] Wed, 21 Mar 2018 21:07:23 UTC (18 KB)
[v2] Thu, 6 Sep 2018 05:09:30 UTC (17 KB)
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