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IRRATIONALITY OF ZEROS OF POLYGAMMA FUNCTIONS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  10 February 2025

PREETI GOYAT Open the ORCID record for PREETI GOYAT [Opens in a new window]
PREETI GOYAT*
Affiliation:
Chennai Mathematical Institute, Sipcot IT Park, Siruseri, Kelambakkam 603103, India
*
e-mail: [email protected]
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Abstract

Our work owes its origin to a recent note of Ram Murty [‘Irrationality of zeros of the digamma function’, Number Theory in Memory of Eduard Wirsing (eds. H. Maier, R. Steuding and J. Steuding) (Springer, Cham, 2023), 237–243], in which he proves that all the zeros of the digamma function are irrational with at most one possible exception. We extend this investigation to higher-order polygamma functions.

Keywords

polygamma functionzerosirrationality

MSC classification

Primary: 11J72: Irrationality; linear independence over a field
Secondary: 11J81: Transcendence (general theory) 11J86: Linear forms in logarithms; Baker's method
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 11
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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