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Barry Brent

Barry Brent

This version is not peer-reviewed

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.

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Subject: Computer Science and Mathematics - Algebra and Number Theory

Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

Submitted:

18 June 2023

Posted:

19 June 2023

Read the latest preprint version here

Alerts

Barry Brent

Barry Brent

This version is not peer-reviewed

Submitted:

18 June 2023

Posted:

19 June 2023

Read the latest preprint version here

Alerts

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.

Keywords:

Subject: Computer Science and Mathematics - Algebra and Number Theory

Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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