Confirm Goldfeld Conjectured for Infinitely Many Elliptic Curves

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Dr. Safwan Aouira
Dr. Hasan Sankari
Ahmad Abdo

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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How to Cite
[1]
Dr. Safwan Aouira, Dr. Hasan Sankari, and Ahmad Abdo , Trans., “Confirm Goldfeld Conjectured for Infinitely Many Elliptic Curves”, IJAM, vol. 6, no. 1, pp. 3–4, Apr. 2026, doi: 10.54105/ijam.A1230.06010426.
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Author Biography

Ahmad Abdo, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.



How to Cite

[1]
Dr. Safwan Aouira, Dr. Hasan Sankari, and Ahmad Abdo , Trans., “Confirm Goldfeld Conjectured for Infinitely Many Elliptic Curves”, IJAM, vol. 6, no. 1, pp. 3–4, Apr. 2026, doi: 10.54105/ijam.A1230.06010426.

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

Z.Kun Li, Quadratic Twists of Elliptic Curves with 3-Selmer Rank 1, https://arxiv.org/abs/1311.5306

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

J.Brudern, K. Kawada, and T.D.Wooley, Additive representation in thin sequences, II: The binary Goldbach problem, Mathematica 47.

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