Article
Version 6
Preserved in Portico This version is not peer-reviewed
On the Constant Terms of Certain Laurent Series
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)
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)
How to cite: Brent, B. On the Constant Terms of Certain Laurent Series. Preprints 2023, 2023061164. https://doi.org/10.20944/preprints202306.1164.v6 Brent, B. On the Constant Terms of Certain Laurent Series. Preprints 2023, 2023061164. https://doi.org/10.20944/preprints202306.1164.v6
Abstract
We study the divisibility properties of the constant terms of certain meromorphic modular forms for Hecke groups. We relate those properties to those of some sequences that have already appeared in the literature. For possible use in later drafts, we show how to invert the map taking a Laurent series $f(x) = 1/x + \sum_{n=0}^{\infty}a_{n+1} x^n$ to the sequence of constant terms of its positive powers. At the end of the article, we construct from elementary arithmetic functions some meromorphic but not necessarily modular functions and study their constant terms.
Keywords
Laurent series; constant term; modular form; integer partition
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (1)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
Commenter: Barry Brent
Commenter's Conflict of Interests: Author
Renamed the corollary to the (former) Theorem 1 as Theorem 1 itself.