算术序列与齐次多项式  

Arithmetic Progressions and Homogeneous Polynomials

作　　者：戴冰[1,2] 黄冬梅[3] 唐春明[3] DAI Bing;HUANG Dongmei;TANG Chunming(Institute of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068 , China;Jiaxiang Foreign Languages School Atached Chengdu No.7 Middle School, Chengdu 610000 , China;College of Mathematic and Inform ation, China West Normal University, Nanchong Sichuan 637009 , China)

机构地区：[1]四川师范大学数学与软件科学学院,成都610068 [2]成都七中嘉祥外国语学校,成都610000 [3]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2017年第2期173-175,226,共4页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11401480)

摘　　要：二次型是研究的一个热点,Alaca等给出了二次型中含有算术序列的充要条件。本文首先考虑齐次多项式中含有算术序列的情况,证明了一类齐次多项式不含有非平凡的算术序列,并进一步考虑包含算术序列的二次型的刻画,给出了二次型含有算术序列的必要条件。Quadratic forms is a hotspot in research.Alaca et al.presents necessary and sufficient conditions for quadratic forms representing some arithmetic progressions.This paper firstly takes homogeneous polynomials into consideration and proves that a class of homogenous polynomials does not represent any non trivial arithmetic pro-gressions.Then,quadratic forms representing arithmetic progressions are considered and necessary conditions are presented.

关 键 词：二次型 二元齐次多项式 算术序列 

分 类 号：O156.5[理学—数学]