ON ASYMPTOTICALLY OPTIMAL TOWERS OVER QUADRATIC FIELDS RELATED TO GAUSS HYPERGEOMETRIC FUNCTIONS-Reference-Cited by-同舟云学术

ON ASYMPTOTICALLY OPTIMAL TOWERS OVER QUADRATIC FIELDS RELATED TO GAUSS HYPERGEOMETRIC FUNCTIONS

Published:2010-08 Issue:05 Volume:06 Page:989-1009
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

HASEGAWA TAKEHIRO¹

Affiliation:

1. Department of Mathematics, School of Education, Waseda University, Tokyo 169-8050, Japan

Abstract

We define two asymptotically optimal towers over quadratic fields, and give the explicit descriptions of the ramification loci and the sets of places splitting completely, which relate to the elliptic modular curves X0(4n) and X0(3n), respectively. Moreover, in the last section, we determine completely the modularity of a tower given by Maharaj and Wulftange in [18].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042110003344

Reference28 articles.

1. On the splitting of places in a tower of function fields meeting the Drinfeld-Vladut bound

2. Towards a Basis for the Space of Regular Functions in a Tower of Function Fields Meeting the Drinfeld-Vladut Bound

3. Asymptotically good towers and differential equations

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