On murmurations — Draconitic Research

Abstract

In the recent paper ``Murmurations", Zubrilina showed that the Fourier coefficients of modular forms follow a certain murmuration pattern. The proof given in ``Murmurations" proceeded by estimating the terms of the Skoruppa-Zagier trace formula. However, a few technical issues arise in the proof, including an omission of certain Chebyshev factors that arise in summations from the Skoruppa-Zagier trace formula. In this work, we address these issues to solidify the proof.

Cite

BibTeX RIS

BibTeX

@misc{nelson2026murmurations,
  title = {{On murmurations}},
  author = {Timothy Nelson and Erick Ross and Maya Wassercug and Hui Xue},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29631},
  eprint = {2609.29631},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29631},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - On murmurations
AU  - Timothy Nelson
AU  - Erick Ross
AU  - Maya Wassercug
AU  - Hui Xue
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.29631
UR  - https://arxiv.org/abs/2609.29631
AB  - In the recent paper ``Murmurations", Zubrilina showed that the Fourier coefficients of modular forms follow a certain murmuration pattern. The proof given in ``Murmurations" proceeded by estimating the terms of the Skoruppa-Zagier trace formula. However, a few technical issues arise in the proof, including an omission of certain Chebyshev factors that arise in summations from the Skoruppa-Zagier trace formula. In this work, we address these issues to solidify the proof.
ER  -