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PreprintarXiv licencearXiv

Zeros of Ramanujan-Like Polynomials

  • Benjamin Fichter
  • Vishal Shah
  • Wiseley Wong
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Abstract

In this paper we study a naturally occurring variant of Ramanujan polynomials with a Bernoulli convolution structure, Sv, related to the double Mordell-Tornheim series. In particular, we prove for even v all zeros of Sv lie on the complex unit circle, and for even v ≥ 4 they are simple with the exception of roots at $1, -1$, which are double roots.

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Cite

BibTeXRIS
BibTeX
@misc{fichter2026zeros,
  title = {{Zeros of Ramanujan-Like Polynomials}},
  author = {Benjamin Fichter and Vishal Shah and Wiseley Wong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07583},
  eprint = {2609.07583},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07583},
}
RIS
TY  - UNPB
TI  - Zeros of Ramanujan-Like Polynomials
AU  - Benjamin Fichter
AU  - Vishal Shah
AU  - Wiseley Wong
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07583
UR  - https://arxiv.org/abs/2609.07583
AB  - In this paper we study a naturally occurring variant of Ramanujan polynomials with a Bernoulli convolution structure, S_v, related to the double Mordell-Tornheim series. In particular, we prove for even v all zeros of S_v lie on the complex unit circle, and for even v ≥ 4 they are simple with the exception of roots at $1, -1$, which are double roots.
ER  -