There are Salem Numbers with Trace –3 and Every Degree At Least 34

Giacomo Cherubini; Pavlo Yatsyna

doi:10.1080/10586458.2024.2337223

There are Salem Numbers with Trace –3 and Every Degree At Least 34

Giacomo Cherubini^*, Pavlo Yatsyna

^*Corresponding author for this work

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

Abstract

We prove that there exist Salem numbers with trace –3 and every even degree (Formula presented.). Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace –3 and degree (Formula presented.), our result is optimal up to possibly the single value 32, for which it is expected there are no such numbers.

Original language	English
Journal	Experimental Mathematics
DOIs	https://doi.org/10.1080/10586458.2024.2337223
Publication status	E-pub ahead of print - 14 Apr 2024
MoE publication type	A1 Journal article-refereed

Keywords

cyclotomic
interlacing
polynomial
Salem number
trace

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10.1080/10586458.2024.2337223Licence: CC BY

Cite this

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title = "There are Salem Numbers with Trace –3 and Every Degree At Least 34",

abstract = "We prove that there exist Salem numbers with trace –3 and every even degree (Formula presented.). Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace –3 and degree (Formula presented.), our result is optimal up to possibly the single value 32, for which it is expected there are no such numbers.",

keywords = "cyclotomic, interlacing, polynomial, Salem number, trace",

author = "Giacomo Cherubini and Pavlo Yatsyna",

note = "Publisher Copyright: {\textcopyright} 2024 Taylor & Francis Group, LLC.",

year = "2024",

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doi = "10.1080/10586458.2024.2337223",

language = "English",

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AU - Cherubini, Giacomo

AU - Yatsyna, Pavlo

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N2 - We prove that there exist Salem numbers with trace –3 and every even degree (Formula presented.). Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace –3 and degree (Formula presented.), our result is optimal up to possibly the single value 32, for which it is expected there are no such numbers.

AB - We prove that there exist Salem numbers with trace –3 and every even degree (Formula presented.). Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace –3 and degree (Formula presented.), our result is optimal up to possibly the single value 32, for which it is expected there are no such numbers.

KW - cyclotomic

KW - interlacing

KW - polynomial

KW - Salem number

KW - trace

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SN - 1058-6458

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JF - Experimental Mathematics

ER -

There are Salem Numbers with Trace –3 and Every Degree At Least 34

Abstract

Keywords

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Hollanti NT: Number-theoretic well-rounded lattices

MATINE_Hollanti_2022-2023: Kvanttiturvallisten hilasalausmenetelmien analyysi ja verifiointi

Hollanti_ICT: Secure Distributed Computation Schemes with Applications to Digitalized Remote Healthcare

Cite this

There are Salem Numbers with Trace –3 and Every Degree At Least 34

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Hollanti NT: Number-theoretic well-rounded lattices

MATINE_Hollanti_2022-2023: Kvanttiturvallisten hilasalausmenetelmien analyysi ja verifiointi

Hollanti_ICT: Secure Distributed Computation Schemes with Applications to Digitalized Remote Healthcare

Cite this