Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8 | Zendy

V. Flammang | Zendy

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Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8

Author(s) -

V. Flammang

Publication year - 2020

Publication title -

mathematics of computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.95

H-Index - 103

eISSN - 1088-6842

pISSN - 0025-5718

DOI - 10.1090/mcom/3580

Subject(s) - mathematics , bounded function , algebraic number , upper and lower bounds , trace (psycholinguistics) , discrete mathematics , combinatorics , measure (data warehouse) , mathematical analysis , philosophy , linguistics , database , computer science

Previously, we established lower bounds for the usual measures (trace, length, Mahler measure) of totally positive algebraic integers, i.e., all of whose conjugates are positive real numbers. We used the method of explicit auxiliary functions and we noticed that the house of most of the totally positive polynomials involved in our functions are bounded by 5.8. Thanks to this observation, we are able to use the same method and give upper bounds for the usual measures of totally positive algebraic integers with house bounded by this value. To our knowledge, theses upper bounds are the first results of this kind.

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