On the Constant Terms of Certain Laurent Series

Barry Brent

doi:10.20944/preprints202306.1164.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 15 June 2023 / Approved: 16 June 2023 / Online: 16 June 2023 (03:45:35 CEST)
Version 2 : Received: 18 June 2023 / Approved: 19 June 2023 / Online: 19 June 2023 (05:14:08 CEST)
Version 3 : Received: 19 June 2023 / Approved: 20 June 2023 / Online: 20 June 2023 (02:58:25 CEST)
Version 4 : Received: 21 June 2023 / Approved: 21 June 2023 / Online: 21 June 2023 (02:46:26 CEST)
Version 5 : Received: 26 June 2023 / Approved: 26 June 2023 / Online: 26 June 2023 (05:23:28 CEST)
Version 6 : Received: 28 June 2023 / Approved: 28 June 2023 / Online: 29 June 2023 (02:07:30 CEST)

We study the divisibility properties of the constant terms of certain meromorphic modular forms for Hecke groups and relate those properties to several O.E.I.S. sequences and several other sequences, the members of which appear in congruences of Ramanujan. At the end of the article, we construct from elementary arithmetic functions some meromorphic but not necessarily modular functions and study their constant terms. For our use in subsequent drafts, we work out a variation of the multinomial theorem convenient for application to single-variable power series.

Laurent series; constant term; modular form; integer partition

Computer Science and Mathematics, Algebra and Number Theory

Comment 1

Received: 19 June 2023
Commenter: Barry Brent
Commenter's Conflict of Interests: Author

Comment: Revised some definitions to avoid division by zero.

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On the Constant Terms of Certain Laurent Series

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