A sharp result on covers
Authors:
Hao Pan and ZhiWei Sun
Journal:
Proc. Amer. Math. Soc. 135 (2007), 35153520
MSC (2000):
Primary 11B25; Secondary 11B75, 11D68, 11R04
Published electronically:
August 15, 2007
MathSciNet review:
2336565
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: Let be a finite system of residue classes which forms an cover of (i.e., every integer belongs to at least members of ). In this paper we show the following sharp result: For any positive integers and , if there is such that the fractional part of is , then there are at least such subsets of . This extends an earlier result of M. Z. Zhang and an extension by Z. W. Sun. Also, we generalize the above result to covers of the integral ring of any algebraic number field with a power integral basis.
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Additional Information
Hao Pan
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
Email:
haopan79@yahoo.com.cn
ZhiWei Sun
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
Email:
zwsun@nju.edu.cn
DOI:
http://dx.doi.org/10.1090/S0002993907088909
PII:
S 00029939(07)088909
Received by editor(s):
January 3, 2006
Received by editor(s) in revised form:
June 3, 2006, and August 25, 2006
Published electronically:
August 15, 2007
Additional Notes:
The second author is responsible for communications and is supported by the National Science Fund for Distinguished Young Scholars (No. 10425103) in China.
Communicated by:
WenChing Winnie Li
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
