On the distribution of analytic ranks of elliptic curves

In this paper, under GRH for elliptic curve L -functions, we give an upper bound for the probability for an elliptic curve with analytic rank ≤ a for a ≥ 11 , and also provide an upper bound of n -th moments of analytic ranks of elliptic curves. These are applications of counting elliptic curves wit...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 305; no. 3
Main Authors Cho, Peter J., Jeong, Keunyoung
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023
Springer Nature B.V
Subjects
Curves
Mathematical analysis
Mathematics
Mathematics and Statistics
Upper bounds
Secondary 11G40
Primary 11G05
Trace formula
11M26
Rank
Elliptic curve
GRH
BSD conjecture
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Summary:In this paper, under GRH for elliptic curve L -functions, we give an upper bound for the probability for an elliptic curve with analytic rank ≤ a for a ≥ 11 , and also provide an upper bound of n -th moments of analytic ranks of elliptic curves. These are applications of counting elliptic curves with local conditions.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-023-03362-y