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October 13, 2025Open Access

Arithmetic properties of generalized Frobenius partitions

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Authors

SAScott AhlgrenCCCruz Castillo

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Overview

Analysis confirms that only specified congruences exist for Frobenius partitions, highlighting connections to modular forms.

Key Points

  • The study confirms no additional congruences exist beyond six for Frobenius partitions of certain types.
  • Foundational work by Ramanujan established initial congruences, which this research builds upon using modern techniques.
  • The integration of computational methods with theoretical insights from modular forms enhances understanding of partition functions.
  • Results indicate the uniqueness of specific modular forms related to m-colored Frobenius partitions for values of m.

Cite This Study

Ahlgren et al. (2025) studied this question.

synapsesocial.com/papers/68ed1896f29694dd1da78b0dhttps://doi.org/10.48550/arxiv.2509.12078
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