Published April 30, 2026
| Version CC-BY-NC-ND 4.0
Journal article
Open
Confirm Goldfeld Conjectured for Infinitely Many Elliptic Curves
Authors/Creators
- 1. Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
- 1. Professor, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
- 2. Professor, Department of Mathematics, Faculty of Science, Lattakia University, Lattakia, Syria.
- 3. Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
Description
Abstract: Goldfeld conjectured: "a positive proportion of quadratic twists of an elliptic curve E/Q have an analytic rank of 1. In this work, we confirm this assertion for infinitely many elliptic curves.
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Additional details
Identifiers
- DOI
- 10.54105/ijam.A1230.06010426
- EISSN
- 2582-8932
Dates
- Accepted
-
2026-04-15Manuscript received on 08 December 2025 | First Revised Manuscript received on 13 December 2025 | Second Revised Manuscript received on 17 March 2026 | Manuscript Accepted on 15 April 2026 | Manuscript published on 30 April 2026.
References
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- R. Barman, A. Narode, and V. Wagh, On the Monogenty of Polynomials with Non-Squarefree Discriminants. https://arxiv.org/pdf/2506.16496
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- H.Darmon, and R.Victor.Arithmetic of elliptic curves and modular forms.CRM Monograph Series.2017. https://www.math.mcgill.ca/darmon/pub/pub.html
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