On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves

The aim of this paper is to analyze the distribution of analytic (and signed) square roots of X values on imaginary quadratic twists of elliptic curves. Given an elliptic curve E of rank zero and prime conductor N, there is a weight-(formula presented) modular form g associated with it such that the...

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Autor principal: Quattrini, P.L.
Formato: JOUR
Materias:
Elliptic curves
Modular forms
Tate-Shafarevich groups
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10586458_v15_n3_p355_Quattrini
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_10586458_v15_n3_p355_Quattrini2023-10-03T16:00:58Z On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves Quattrini, P.L. Elliptic curves Modular forms Tate-Shafarevich groups The aim of this paper is to analyze the distribution of analytic (and signed) square roots of X values on imaginary quadratic twists of elliptic curves. Given an elliptic curve E of rank zero and prime conductor N, there is a weight-(formula presented) modular form g associated with it such that the d-coefficient of g is related to the value at s = 1 of the L-series of the (−d)-quadratic twist of the elliptic curve E. Assuming the Birch and Swinnerton-Dyer conjecture, we can then calculate for a large number of integers d the order of X of the (−d)-quadratic twist of E and analyze their distribution. © A K Peters, Ltd. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10586458_v15_n3_p355_Quattrini
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Elliptic curves
Modular forms
Tate-Shafarevich groups
spellingShingle Elliptic curves
Modular forms
Tate-Shafarevich groups
Quattrini, P.L.
On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves
topic_facet Elliptic curves
Modular forms
Tate-Shafarevich groups
description The aim of this paper is to analyze the distribution of analytic (and signed) square roots of X values on imaginary quadratic twists of elliptic curves. Given an elliptic curve E of rank zero and prime conductor N, there is a weight-(formula presented) modular form g associated with it such that the d-coefficient of g is related to the value at s = 1 of the L-series of the (−d)-quadratic twist of the elliptic curve E. Assuming the Birch and Swinnerton-Dyer conjecture, we can then calculate for a large number of integers d the order of X of the (−d)-quadratic twist of E and analyze their distribution. © A K Peters, Ltd.
format JOUR
author Quattrini, P.L.
author_facet Quattrini, P.L.
author_sort Quattrini, P.L.
title On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves
title_short On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves
title_full On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves
title_fullStr On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves
title_full_unstemmed On the distribution of analytic (Formula presented) values on quadratic twists of elliptic curves
title_sort on the distribution of analytic (formula presented) values on quadratic twists of elliptic curves
url http://hdl.handle.net/20.500.12110/paper_10586458_v15_n3_p355_Quattrini
work_keys_str_mv AT quattrinipl onthedistributionofanalyticformulapresentedvaluesonquadratictwistsofellipticcurves
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