On universal elliptic curves over Igusa curves

D. L. Ulmer

doi:10.1007/BF01234424

On universal elliptic curves over Igusa curves

D. L. Ulmer

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Abstract

The purpose of this note is to introduce the arithmetic, study of the universal elliptic curve over Igusa curves. Specifically, its Hasse-Weil L-function is computed in terms of modular forms and is shown to have interesting zeros. Explicit examples are presented for which the Birch and Swinnerton-Dyer conjecture is verified.

Original language	English (US)
Pages (from-to)	377-391
Number of pages	15
Journal	Inventiones Mathematicae
Volume	99
Issue number	1
DOIs	https://doi.org/10.1007/BF01234424
State	Published - Dec 1990
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/BF01234424

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title = "On universal elliptic curves over Igusa curves",

abstract = "The purpose of this note is to introduce the arithmetic, study of the universal elliptic curve over Igusa curves. Specifically, its Hasse-Weil L-function is computed in terms of modular forms and is shown to have interesting zeros. Explicit examples are presented for which the Birch and Swinnerton-Dyer conjecture is verified.",

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AB - The purpose of this note is to introduce the arithmetic, study of the universal elliptic curve over Igusa curves. Specifically, its Hasse-Weil L-function is computed in terms of modular forms and is shown to have interesting zeros. Explicit examples are presented for which the Birch and Swinnerton-Dyer conjecture is verified.

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On universal elliptic curves over Igusa curves

Abstract

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