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학술저널

REMARK ON THE MEAN VALUE OF L( ½,x) IN THE HYPERELLIPTIC ENSEMBLE

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Let A = Fq[T] be a polynomial ring over Fq. In this paper we determine an asymptotic mean value of quadratic Dirich- let L-functions L(s; °D) at the central point s = 12 , where D runs over all monic square-free polynomials of even degree in A and ° isa generator of F¤ q .

1. Introduction and statement of results

2. Preliminaries

3. Proof of main theorem

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