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Möbius Randomness Law for Frobenius Traces of Ordinary Curves

Part of: Arithmetic algebraic geometry Sequences and sets Diophantine approximation, transcendental number theory Exponential sums and character sums

Published online by Cambridge University Press:  15 May 2020

Min Sha  and
Igor E. Shparlinski
Min Sha*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia e-mail: igor.shparlinski@unsw.edu.au
Igor E. Shparlinski
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia e-mail: igor.shparlinski@unsw.edu.au
*
e-mail: shamin2010@gmail.com
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Abstract

Recently E. Bombieri and N. M. Katz (2010) 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 Möbius randomness law quantitatively for the normalised form of Frobenius traces.

Keywords

Möbius randomness lawsmooth projective curveFrobenius traceFrobenius angle

MSC classification

Primary: 11B37: Recurrences
Secondary: 11G20: Curves over finite and local fields 11J25: Diophantine inequalities 11J86: Linear forms in logarithms; Baker's method 11L07: Estimates on exponential sums

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 192 - 203
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

During the preparation of this paper, the first author was supported by the Australian Research Council Grant DE190100888, and the second author was partially supported by the Australian Research Council Grant DP180100201.

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