2021/08/02 by Agbolade Akande, Robert Schneider, Akande, A. P. +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2108.00840
openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent work, M. Just and the second author defined a class of "semi-modular forms" on \mathbb C, in analogy with classical modular forms, that are "half modular" in a particular sense; and constructed families of such functions as Eisenstein-like series using symmetries related to integer partitions. Looking for further natural examples of semi-modular behavior, here we construct a family of Eisenstein-like series to produce semi-modular forms, using symmetries related to Fibonacci numbers instead of partitions. We then consider other Lucas sequences that yield semi-modular forms.