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This is a Quantitative Study study.

October 17, 2025Open Access

Recurrence relations satisfied by some arithmetic groups

Key Points

Modular traces values are fully determined for prime power levels, leveraging recurrence relations.
Key findings include established relations for the Hauptmodul of genus zero in arithmetic groups.
The analysis of additional recursions reveals how these relations can organize modular trace values.
Implications suggest improved understanding of modular traces in arithmetic structures and their complexities.

Abstract

Abstract Recently, recurrence relations satisfied by the modular traces of the Hauptmodul for Γ 0 (N) ₀ (N) of genus zero have been established. However, these relations do not determine all values of the modular traces. In this study, we examine additional recursions and demonstrate that the values of the modular traces are fully determined for prime power levels.

Recurrence relations satisfied by some arithmetic groups

Key Points

Abstract

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