M\"obius Randomness Law for Frobenius Traces
Min Sha, Igor E. Shparlinski
TL;DR
This paper proves a quantitative version of the M"obius randomness law for normalized Frobenius traces, linking algebraic curve properties with number-theoretic randomness concepts.
Contribution
It extends previous work by Bombieri and Katz, providing a new quantitative understanding of Frobenius trace distributions.
Findings
Established the M"obius randomness law for Frobenius traces
Connected algebraic curve properties with number-theoretic randomness
Provided quantitative bounds for the distribution of Frobenius traces
Abstract
Recently E. Bombieri and N. M. Katz (2010) have demonstrated that several well-known results about the distribution of values of linear recurrence sequences lead to interesting statements for Frobenius traces of algebraic curves. Here we continue this line of study and establish the M\"obius randomness law quantitatively for the normalised form of Frobenius traces.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry