Chebyshev's bias in Galois extensions of global function fields

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We study Chebyshev's bias in a finite, possibly nonabelian. Galois extension of global function fields. We show that, when the extension is geometric and satisfies a certain property, called, Linear Independence (LI), the less square elements a conjugacy class of the Galois group has, the more primes there are whose Frobenius conjugacy classes are equal to the conjugacy class. Our results are in line with the previous work of Rubinstein and Sarnak in the number field case and that of the first-named author in the case of polynomial rings over finite fields. We also prove, under LI, the necessary and sufficient conditions for a certain limiting distribution to be symmetric, following the method of Rubinstein and Sarnak. Examples are provided where LI is proved to hold true and is violated. Also, we study the case when the Galois extension is a scalar field extension and describe the complete result of the prime number race in that case. (C) 2011 Elsevier Inc. All rights reserved
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2011-10
Language
English
Article Type
Article
Keywords

QUADRATIC TWISTS

Citation

JOURNAL OF NUMBER THEORY, v.131, no.10, pp.1875 - 1886

ISSN
0022-314X
DOI
10.1016/j.jnt.2011.03.011
URI
http://hdl.handle.net/10203/213012
Appears in Collection
MA-Journal Papers(저널논문)
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