Browse

Representations by a binary quadratic form with class number 3
류수가 3인 이변수 이차형식의 표현

Cited 0 time in Web of Science Cited 0 time in Scopus
Authors
최재민
Advisor
오병권
Major
자연과학대학 수리과학부
Issue Date
2013-02
Publisher
서울대학교 대학원
Description
학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 오병권.
Abstract
For integers a, b, c, the homogeneous quadratic polynomial f(x,y)=ax^2+bxy+cy^2 is called a binary quadratic form. In this thesis, we will give a closed formula on the number of integral solutions of x^2+27y^2=n for any integer n. To do this, we follow the framework given by Min and Oh, where they considered the binary form x^2+32y^2. In section 2, we briefly survey on the theory of binary quadratic forms and give some lemmas which are needed in the later. In section 3, we consider the case when n is a prime power. In section 4, we consider the case when n is any integer relatively prime to 6. In section 5, we summarize everything and give a complete formula on the number of solutions of the above equation.
Language
English
URI
http://hdl.handle.net/10371/131459
Files in This Item:
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Master's Degree_수리과학부)
  • mendeley

Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse