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1. Distribution of zeta zeroes for abelian covers of algebraic curves over a finite field.

Author

Xiong, Maosheng

Subjects
*GAUSSIAN distribution, *ABELIAN groups, *ZETA functions, *ZERO (The number), *ALGEBRAIC curves, *FINITE fields
Abstract

For a function field k over a finite field with F q as the field of constants, and a finite abelian group G whose exponent divides q − 1 , we study the distribution of zeta zeroes for a random G -extension of k , ordered by the degree of conductors. We prove that when the degree goes to infinity, the number of zeta zeroes lying in a prescribed arc is uniformly distributed and the variance follows a Gaussian distribution. [ABSTRACT FROM AUTHOR]

Published
2015
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