A mean value theorem for orders of degree zero divisor class groups of quadratic extensions over a function field

Takashi Taniguchi

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A mean value theorem for orders of degree zero divisor class groups of quadratic extensions over a function field

Takashi Taniguchi

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Abstract

Let $k$ be a function field of one variable over a finite field with the characteristic not equal to two. In this paper, we consider the prehomogeneous representation of the space of binary quadratic forms over $k$. We have two main results. The first result is on the principal part of the global zeta function associated with the prehomogeneous vector space. The second result is on a mean value theorem for degree zero divisor class groups of quadratic extensions over $k$, which is a consequence of the first one.

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Takashi Taniguchi. 2002-03-14. A mean value theorem for orders of degree zero divisor class groups of quadratic extensions over a function field. https://arxiv.org/abs/math/0203132

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