scholarly journals On a mean value formula for the approximate functional equation of $\bm{\zeta(s)}$ in the critical strip

2005 ◽  
Vol 57 (2) ◽  
pp. 513-521
Author(s):  
Shao-Ji FENG
Keyword(s):  
Functional Equation ◽  
Mean Value ◽  
Critical Strip ◽  
Approximate Functional Equation ◽  
Mean Value Formula

scholarly journals ON THE RANKIN–SELBERG ZETA FUNCTION

2012 ◽  
Vol 93 (1-2) ◽  
pp. 101-113
Author(s):  
ALEKSANDAR IVIĆ
Keyword(s):  
Functional Equation ◽  
Zeta Function ◽  
Critical Line ◽  
Critical Strip ◽  
Approximate Functional Equation ◽  
Selberg Zeta Function

AbstractWe obtain the approximate functional equation for the Rankin–Selberg zeta function in the critical strip and, in particular, on the critical line $\operatorname {Re} s= \frac {1}{2}$.

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].

Sign in / Sign up

Export Citation Format

Share Document