Discussion on some conjectures regarding the periodicity of sign patterns of certain infinite products involving the Rogers-Ramanujan Continued Fractions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909568047513600 |
|---|---|
| author | Ghoshal, Suparno Jana, Arijit |
| author_facet | Ghoshal, Suparno Jana, Arijit |
| contents | Let $R(q)$ denote the Rogers-Ramanujan continued fraction. Define $$ \frac{1}{R^5(q)}=\displaystyle \sum_{n=0}^{\infty}A(n)q^{n} \quad \text{and} \quad R^5(q)=\displaystyle\sum_{n=0}^{\infty}B(n)q^{n}.$$ Baruah and Sarma recently posed conjectures regarding the sign patterns of $A(5n), B(5n)$ for $n\geq 0.$ In this paper, we show that these conjectures do not hold for $n=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discussion on some conjectures regarding the periodicity of sign patterns of certain infinite products involving the Rogers-Ramanujan Continued Fractions Ghoshal, Suparno Jana, Arijit Number Theory Let $R(q)$ denote the Rogers-Ramanujan continued fraction. Define $$ \frac{1}{R^5(q)}=\displaystyle \sum_{n=0}^{\infty}A(n)q^{n} \quad \text{and} \quad R^5(q)=\displaystyle\sum_{n=0}^{\infty}B(n)q^{n}.$$ Baruah and Sarma recently posed conjectures regarding the sign patterns of $A(5n), B(5n)$ for $n\geq 0.$ In this paper, we show that these conjectures do not hold for $n=0$. |
| title | Discussion on some conjectures regarding the periodicity of sign patterns of certain infinite products involving the Rogers-Ramanujan Continued Fractions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.17950 |