Extreme central L-values of almost prime quadratic twists of elliptic curves

Shenghao Hua; Bingrong Huang

doi:10.1007/s11425-022-2216-y

Extreme central L-values of almost prime quadratic twists of elliptic curves

Shenghao Hua, Bingrong Huang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we prove the extreme values of L-functions at the central point for almost prime quadratic twists of an elliptic curve. As an application, we get the extreme values for the Tate-Shafarevich groups in the quadratic twist family of an elliptic curve under the Birch and Swinnerton-Dyer conjecture.

Original language	English
Journal	Science China Mathematics
DOIs	https://doi.org/10.1007/s11425-022-2216-y
State	Accepted/In press - 2023
Externally published	Yes

Keywords

11F67
almost prime
central L-value
elliptic curve
extreme value
quadratic twist

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10.1007/s11425-022-2216-y

Cite this

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title = "Extreme central L-values of almost prime quadratic twists of elliptic curves",

abstract = "In this paper, we prove the extreme values of L-functions at the central point for almost prime quadratic twists of an elliptic curve. As an application, we get the extreme values for the Tate-Shafarevich groups in the quadratic twist family of an elliptic curve under the Birch and Swinnerton-Dyer conjecture.",

keywords = "11F67, almost prime, central L-value, elliptic curve, extreme value, quadratic twist",

author = "Shenghao Hua and Bingrong Huang",

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year = "2023",

doi = "10.1007/s11425-022-2216-y",

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AU - Huang, Bingrong

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AB - In this paper, we prove the extreme values of L-functions at the central point for almost prime quadratic twists of an elliptic curve. As an application, we get the extreme values for the Tate-Shafarevich groups in the quadratic twist family of an elliptic curve under the Birch and Swinnerton-Dyer conjecture.

KW - 11F67

KW - almost prime

KW - central L-value

KW - elliptic curve

KW - extreme value

KW - quadratic twist

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JO - Science China Mathematics

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Extreme central L-values of almost prime quadratic twists of elliptic curves

Abstract

Keywords

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