The mean value formula for the approximate functional equation of ?2(s) in the critical strip II

1996 ◽  
Vol 67 (2) ◽  
pp. 126-133
Author(s):  
Isao Kiuchi
Keyword(s):  
Functional Equation ◽  
Mean Value ◽  
Critical Strip ◽  
Approximate Functional Equation ◽  
The Mean ◽  
Mean Value Formula

scholarly journals A NOTE ON THE MEAN VALUE OF L-FUNCTIONS IN FUNCTION FIELDS

2012 ◽  
Vol 08 (07) ◽  
pp. 1725-1740 ◽  
Author(s):  
JULIO ANDRADE
Keyword(s):  
Functional Equation ◽  
Asymptotic Formula ◽  
Finite Field ◽  
Class Number ◽  
Function Fields ◽  
Hyperelliptic Curves ◽  
Mean Value ◽  
Approximate Functional Equation ◽  
The Mean

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].

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