Cyclotomic coefficients: Gaps and jumps

Oana Maria Camburu; Emil Alexandru Ciolan; Florian Luca; Pieter Moree; Igor E. Shparlinski

doi:10.1016/j.jnt.2015.11.020

Cyclotomic coefficients: Gaps and jumps

Oana Maria Camburu, Emil Alexandru Ciolan^*, Florian Luca, Pieter Moree, Igor E. Shparlinski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduce several new techniques that have never been used in this area.

Original language	English
Pages (from-to)	211-237
Number of pages	27
Journal	Journal of Number Theory
Volume	163
DOIs	https://doi.org/10.1016/j.jnt.2015.11.020
Publication status	Published - 1 Jun 2016
Externally published	Yes

Keywords

Coefficients of cyclotomic polynomials
Double Kloosterman sums
Numerical semigroups
Products of primes

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10.1016/j.jnt.2015.11.020

Cite this

@article{ac3e1b03e6d74e5aa98d94f166a06f92,

title = "Cyclotomic coefficients: Gaps and jumps",

abstract = "We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduce several new techniques that have never been used in this area.",

keywords = "Coefficients of cyclotomic polynomials, Double Kloosterman sums, Numerical semigroups, Products of primes",

author = "Camburu, {Oana Maria} and Ciolan, {Emil Alexandru} and Florian Luca and Pieter Moree and Shparlinski, {Igor E.}",

year = "2016",

month = jun,

day = "1",

doi = "10.1016/j.jnt.2015.11.020",

language = "English",

volume = "163",

pages = "211--237",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Cyclotomic coefficients

T2 - Gaps and jumps

AU - Camburu, Oana Maria

AU - Ciolan, Emil Alexandru

AU - Luca, Florian

AU - Moree, Pieter

AU - Shparlinski, Igor E.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduce several new techniques that have never been used in this area.

AB - We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduce several new techniques that have never been used in this area.

KW - Coefficients of cyclotomic polynomials

KW - Double Kloosterman sums

KW - Numerical semigroups

KW - Products of primes

UR - http://www.scopus.com/inward/record.url?scp=84954521494&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP130100237

UR - http://purl.org/au-research/grants/arc/DP140100118

U2 - 10.1016/j.jnt.2015.11.020

DO - 10.1016/j.jnt.2015.11.020

M3 - Article

AN - SCOPUS:84954521494

SN - 0022-314X

VL - 163

SP - 211

EP - 237

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Cyclotomic coefficients: Gaps and jumps

Abstract

Keywords

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New Applications of Additive Combinatorics in Number Theory and Graph Theory

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Cyclotomic coefficients: Gaps and jumps

Abstract

Keywords

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New Applications of Additive Combinatorics in Number Theory and Graph Theory

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