Linear independence of harmonic numbers over the field of algebraic numbers

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DC Field	Value	Language
dc.contributor.author	Chatterjee, T.	-
dc.contributor.author	Dhillon, S.	-
dc.date.accessioned	2020-03-13T10:54:21Z	-
dc.date.available	2020-03-13T10:54:21Z	-
dc.date.issued	2020-03-13	-
dc.identifier.uri	http://localhost:8080/xmlui/handle/123456789/1527	-
dc.description.abstract	Let Hn = n k=1 1 k be the nth harmonic number. Euler extended it to complex arguments and defined Hr for any complex number r except for the negative integers. In this paper, we give a new proof of the transcendental nature of Hr for rational r. For some special values of q > 1, we give an upper bound for the number of linearly independent harmonic numbers Ha/q with 1 ≤ a ≤ q over the field of algebraic numbers. Also, for any finite set of odd primes J with \|J \| = n, define WJ = Q − span of H1, Ha j i /qi \|1 ≤ a ji ≤ qi − 1, 1 ≤ ji ≤ qi − 1, ∀qi ∈ J . Finally, we show that dim Q WJ = n i=1 qi∈J φ(qi) 2	en_US
dc.language.iso	en_US	en_US
dc.subject	Baker’s Theory	en_US
dc.subject	Digamma function	en_US
dc.subject	Galois theory	en_US
dc.subject	Gauss formula	en_US
dc.subject	Harmonic Numbers	en_US
dc.subject	Linear forms in logarithm	en_US
dc.subject	Linear independence	en_US
dc.title	Linear independence of harmonic numbers over the field of algebraic numbers	en_US
dc.type	Article	en_US
Appears in Collections:	Year-2020

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