BROWSE

Related Scientist

kim,dohyeong's photo.

kim,dohyeong
기하학수리물리연구단
more info

ITEM VIEW & DOWNLOAD

A modular approach to cubic Thue-Mahler equations

Cited 1 time in webofscience Cited 0 time in scopus
1,295 Viewed 249 Downloaded
Title
A modular approach to cubic Thue-Mahler equations
Author(s)
Dohyeong Kim
Publication Date
2017-05
Journal
MATHEMATICS OF COMPUTATION, v.86, no.305, pp.1435 - 1471
Publisher
AMER MATHEMATICAL SOC
Abstract
Let h(x, y) be a non-degenerate binary cubic form with integral coefficients, and let S be an arbitrary finite set of prime numbers. By a classical theorem of Mahler, there are only finitely many pairs of relatively prime integers x, y such that h(x, y) is an S-unit. In the present paper, we reverse a well-known argument, which seems to go back to Shafarevich, and use the modularity of elliptic curves over Q to give upper bounds for the number of solutions of such a Thue-Mahler equation. In addition, our methods give an effective method for determining all solutions, and we use Cremona's Elliptic Curve Database to give a wide range of numerical examples. © 2016 American Mathematical Society
URI
https://pr.ibs.re.kr/handle/8788114/3424
DOI
10.1090/mcom/3139
ISSN
0025-5718
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
Files in This Item:
S0025-5718-2016-03139-7.pdfDownload

qrcode

  • facebook

    twitter

  • Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
해당 아이템을 이메일로 공유하기 원하시면 인증을 거치시기 바랍니다.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse