Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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REMARK ON THE MEAN VALUE OF L(½, χ) IN THE HYPERELLIPTIC ENSEMBLE

  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • Received : 2013.06.10
  • Accepted : 2013.10.18
  • Published : 2014.02.15
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Abstract

Let $\mathbb{A}=\mathbb{F}_q[T]$ be a polynomial ring over $\mathbb{F}_q$. In this paper we determine an asymptotic mean value of quadratic Dirich-let L-functions L(s, ${\chi}_{{\gamma}D}$) at the central point s=$\frac{1}{2}$, where D runs over all monic square-free polynomials of even degree in $\mathbb{A}$ and ${\gamma}$ is a generator of $\mathbb{F}_q^*$.

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References

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