scholarly journals Mean value of the class number in function fields revisited

2018 ◽  
Vol 187 (4) ◽  
pp. 577-602
Author(s):  
Julio C. Andrade ◽  
Hwanyup Jung
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Mean Value

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].

scholarly journals Extremal behaviour of ± 1-valued completely multiplicative functions in function fields

2021 ◽  
Vol 56 (1) ◽  
pp. 79-94
Author(s):  
Nikola Lelas ◽  
Keyword(s):  
Rational Function ◽  
Finite Fields ◽  
Function Fields ◽  
Mean Value ◽  
Multiplicative Functions ◽  
Irreducible Polynomials ◽  
Liouville Function ◽  
The Mean

We investigate the classical Pólya and Turán conjectures in the context of rational function fields over finite fields 𝔽q. Related to these two conjectures we investigate the sign of truncations of Dirichlet L-functions at point s=1 corresponding to quadratic characters over 𝔽q[t], prove a variant of a theorem of Landau for arbitrary sets of monic, irreducible polynomials over 𝔽q[t] and calculate the mean value of certain variants of the Liouville function over 𝔽q[t].

scholarly journals On the Gauss mean-value formula for class number

1998 ◽  
Vol 151 ◽  
pp. 199-208 ◽  
Author(s):  
Fernando Chamizo ◽  
Henryk Iwaniec
Keyword(s):  
Class Number ◽  
Approximate Formula ◽  
Error Term ◽  
Exponential Sums ◽  
Mean Value ◽  
Point Problem ◽  
Class Number Formula ◽  
Modern Notation ◽  
Number Formula ◽  
Mean Value Formula

Abstract.In his masterwork Disquisitiones Arithmeticae, Gauss stated an approximate formula for the average of the class number for negative discriminants. In this paper we improve the known estimates for the error term in Gauss approximate formula. Namely, our result can be written as for every ∊ > 0, where H(−n) is, in modern notation, h(−4n). We also consider the average of h(−n) itself obtaining the same type of result.Proving this formula we transform firstly the problem in a lattice point problem (as probably Gauss did) and we use a functional equation due to Shintani and Dirichlet class number formula to express the error term as a sum of character and exponential sums that can be estimated with techniques introduced in a previous work on the sphere problem.

A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn

2006 ◽  
Vol 49 (3) ◽  
pp. 448-463 ◽  
Author(s):  
Allison M. Pacelli
Keyword(s):  
Lower Bound ◽  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Prime Degree ◽  
Cyclic Function ◽  
Quadratic Function Fields

AbstractIn this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.

scholarly journals Function fields of class number one

2015 ◽  
Vol 154 ◽  
pp. 375-379 ◽  
Author(s):  
Qibin Shen ◽  
Shuhui Shi
Keyword(s):  
Class Number ◽  
Function Fields
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