Remark on average of class numbers of function fields
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Let k = Fq(T) be a rational function field over the finitefield Fq, where q is a power of an odd prime number, and A = Fq[T]. Let γ be a generator of F*q. Let Hn be the subset of A consisting ofmonic square-free polynomials of degree n. In this paper we obtainan asymptotic formula for the mean value of L(1,XγD) and calculatethe average value of the ideal class number hγD when the average istaken over D ∈ H2g+2.
Abstract
Let k = Fq(T) be a rational function field over the finitefield Fq, where q is a power of an odd prime number, and A = Fq[T]. Let γ be a generator of F*q. Let Hn be the subset of A consisting ofmonic square-free polynomials of degree n. In this paper we obtainan asymptotic formula for the mean value of L(1,XγD) and calculatethe average value of the ideal class number hγD when the average istaken over D ∈ H2g+2.
참고문헌 (5)
- J.C. Andrade, "A note on the mean value of L-functions in function fields", Int. J. Number Theory, 08(12), pp.1725~1740 (2012)
- J.C. Andrade, "The mean value of L(1", 2, X) in the hyperelliptic ensemble, 2012, pp.132(12), 2793~2816
- J. Hoffstein, "Average values of L-series in function fields", J. Reine Angew. Math, 426, pp.117~150 (1992)
- H. Jung, "A note on the mean value of L(1, X) in the hyperelliptic ensemble", Int. J. Number Theory
- M. Rosen, "Number theory in function fields, In Graduate Texts in Mathematics 210" (2002), Springer-Verlag