Mobius function in short intervals for function fields

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Let mu(A) be the Mobius function defined in a polynomial ring F-q[T] with coefficients in the finite field F-q of q elements (q is odd). In this paper, we present a function field version of partial progress toward a conjecture of Good and Churchhouse. We calculate the mean and the large q limit of the variance of partial sums of the Mobius function on short intervals. Our calculation closely follows the framework of a recent work of Keating and Rudnick, where they consider the distribution of the von Mangoldt function in function fields.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2015-07
Language
English
Article Type
Article
Citation

FINITE FIELDS AND THEIR APPLICATIONS, v.34, pp.235 - 249

ISSN
1071-5797
DOI
10.1016/j.ffa.2015.02.002
URI
http://hdl.handle.net/10203/198538
Appears in Collection
MA-Journal Papers(저널논문)
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