# [Goldfeld's analytic density conjecture and the 2-converse for elliptic curves](paper.pdf)

**Author:** OpenAI

**Date:** October 7, 2026

## Citation

```bibtex
@misc{OAI:Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curves-October-7-2026,
  author = {{OpenAI}},
  title = {{Goldfeld's analytic density conjecture and the $2$-converse for elliptic curves}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curves-October-7-2026/paper.pdf}{OAI:Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curves-October-7-2026}},
  year = {2026}
}
```

## Version note

This version updates citations to revised manuscripts in this collection; see the [previous version](../Goldfelds-analytic-density-conjecture-and-the-2-converse-for-elliptic-curves-September-23-2026/paper.pdf).