Gaussian binomial coefficients modulo cyclotomic polynomials

Yan Li; Daeyeoul Kim; Lianrong Ma

doi:10.1016/j.jnt.2016.04.005

Gaussian binomial coefficients modulo cyclotomic polynomials

Yan Li
, Daeyeoul Kim^*
, Lianrong Ma

^*Corresponding author for this work

Department of Mathematics

China Agricultural University
National Institute for Mathematical Sciences
Tsinghua University

Research output: Contribution to journal › Journal article › peer-review

1 Scopus citations

Abstract

In this paper, we give q-analogies of classical Kummer, Lucas and ASH (Anton, Stickelberger, Hensel)'s results on binomial coefficients modulo primes. Our results generalize the previous result by T. Cai (2001) [1].

Original language	English
Pages (from-to)	154-166
Number of pages	13
Journal	Journal of Number Theory
Volume	168
DOIs	https://doi.org/10.1016/j.jnt.2016.04.005
State	Published - 2016.11.1

Keywords

Binomial coefficients
Congruence
Cyclotomic polynomials
Gaussian binomial coefficients
Q-Series

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10.1016/j.jnt.2016.04.005

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@article{e9f4b7bbc02d437dba341eb3e5b9dcd7,

title = "Gaussian binomial coefficients modulo cyclotomic polynomials",

abstract = "In this paper, we give q-analogies of classical Kummer, Lucas and ASH (Anton, Stickelberger, Hensel)'s results on binomial coefficients modulo primes. Our results generalize the previous result by T. Cai (2001) [1].",

keywords = "Binomial coefficients, Congruence, Cyclotomic polynomials, Gaussian binomial coefficients, Q-Series",

author = "Yan Li and Daeyeoul Kim and Lianrong Ma",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

month = nov,

day = "1",

doi = "10.1016/j.jnt.2016.04.005",

language = "English",

volume = "168",

pages = "154--166",

journal = "Journal of Number Theory",

issn = "0022-314X",

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TY - JOUR

T1 - Gaussian binomial coefficients modulo cyclotomic polynomials

AU - Li, Yan

AU - Kim, Daeyeoul

AU - Ma, Lianrong

PY - 2016/11/1

Y1 - 2016/11/1

N2 - In this paper, we give q-analogies of classical Kummer, Lucas and ASH (Anton, Stickelberger, Hensel)'s results on binomial coefficients modulo primes. Our results generalize the previous result by T. Cai (2001) [1].

AB - In this paper, we give q-analogies of classical Kummer, Lucas and ASH (Anton, Stickelberger, Hensel)'s results on binomial coefficients modulo primes. Our results generalize the previous result by T. Cai (2001) [1].

KW - Binomial coefficients

KW - Congruence

KW - Cyclotomic polynomials

KW - Gaussian binomial coefficients

KW - Q-Series

UR - https://www.scopus.com/pages/publications/84973137899

U2 - 10.1016/j.jnt.2016.04.005

DO - 10.1016/j.jnt.2016.04.005

M3 - Journal article

AN - SCOPUS:84973137899

SN - 0022-314X

VL - 168

SP - 154

EP - 166

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Gaussian binomial coefficients modulo cyclotomic polynomials

Abstract

Keywords

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