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September 29, 20250 citationsOpen Access

Sign Patterns and Congruences in Rogers-Ramanujan Infinite Products

Sign Patterns and Congruences of certain infinite products involving the Rogers-Ramanujan continued fraction

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Authors

NBNayandeep Deka BaruahASAbhishek Sarma

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Overview

Analysis reveals positive and negative coefficient patterns in infinite products, highlighting congruences.

Key Points

  • Positive coefficients are found for A(5n+1), A(5n+2), and A(5n+3), while A(5n+4) is negative.
  • Congruences show A(9n+4) is zero modulo 3, A(16n+13) is zero modulo 4, and A(15n+r) is zero modulo 15.
  • The study explores the behavior of coefficients in the context of the Rogers-Ramanujan continued fraction.
  • Analysis of these properties can lead to deeper insights in number theory and related areas.

Cite This Study

Baruah et al. (2025) studied this question.

synapsesocial.com/papers/68da58c9c1728099cfd10adfhttps://doi.org/10.48550/arxiv.2503.08517
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