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Lucas congruences using modular forms
- Publication Year :
- 2024
-
Abstract
- In this work, we prove that a sequence arising from modular forms under some prescribed conditions for $\Gamma$ that is $\Gamma_{0}(N)$ or an Atkin--Lehner extension of $\Gamma_{0}(N)$ must satisfy the Lucas congruences modulo any prime. As an implication, we completely affirm all the conjectural Lucas congruences that were recently posed by Cooper and reinterpret a number of known results.<br />Comment: 9 pages
- Subjects :
- Mathematics - Number Theory
11F03, 11F11
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.16616
- Document Type :
- Working Paper