An asymptotic formula for the sum ∑ L(1, χ) is established for a family of hyperelliptic curves of genus g over a fixed finite field 𝔽q as g → ∞ making use of the analog of the approximate functional equation for such L-functions. As a corollary, we obtain a formula for the average of the class number of the associated rings [Formula: see text].
An Improvement on the Mean Value Formula for the Approximate Functional Equation of the Square of the Riemann Zeta-Function