2 results
On lower bounds for the Ihara constants
$A(2)$ and 
$A(3)$
- Part of
-
- Journal:
- Compositio Mathematica / Volume 149 / Issue 7 / July 2013
- Published online by Cambridge University Press:
- 03 May 2013, pp. 1108-1128
- Print publication:
- July 2013
-
- Article
-
- You have access
- Export citation
-
Let
$ \mathcal{X} $ be a curve over 
${ \mathbb{F} }_{q} $ and let 
$N( \mathcal{X} )$, 
$g( \mathcal{X} )$ be its number of rational points and genus respectively. The Ihara constant 
$A(q)$ is defined by 
$A(q)= {\mathrm{lim~sup} }_{g( \mathcal{X} )\rightarrow \infty } N( \mathcal{X} )/ g( \mathcal{X} )$. In this paper, we employ a variant of Serre’s class field tower method to obtain an improvement of the best known lower bounds on 
$A(2)$ and 
$A(3)$.
Asymptotic Behavior of Optimal Circle Packings in a Square
-
- Journal:
- Canadian Mathematical Bulletin / Volume 42 / Issue 3 / 01 September 1999
- Published online by Cambridge University Press:
- 20 November 2018, pp. 380-385
- Print publication:
- 01 September 1999
-
- Article
-
- You have access
- Export citation
-
A lower bound on the number of points that can be placed in a square of side
$\sigma$ such that no two points are within unit distance from each other is proven. The result is constructive, and the series of packings obtained contains many conjecturally optimal packings.
