The local root number of elliptic curves with wild ramification

Shinichi Kobayashi

doi:10.1007/s002080200318

The local root number of elliptic curves with wild ramification

Shinichi Kobayashi

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

18 Citations (Scopus)

Abstract

Let E be an elliptic curve over a number field F. The root number is conjecturally the sign of the functional equation of L-function of E/F. It is defined as the product of local signs over all places of F. The purpose of this paper is to describe this local sign by the coefficients of a Weierstraß equation of E.

Original language	English
Pages (from-to)	609-623
Number of pages	15
Journal	Mathematische Annalen
Volume	323
Issue number	3
DOIs	https://doi.org/10.1007/s002080200318
Publication status	Published - Dec 1 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

Access to Document

10.1007/s002080200318

Cite this

@article{53594b5026ef4ccbabe9ef57f7a61da8,

title = "The local root number of elliptic curves with wild ramification",

abstract = "Let E be an elliptic curve over a number field F. The root number is conjecturally the sign of the functional equation of L-function of E/F. It is defined as the product of local signs over all places of F. The purpose of this paper is to describe this local sign by the coefficients of a Weierstra{\ss} equation of E.",

author = "Shinichi Kobayashi",

year = "2002",

month = dec,

day = "1",

doi = "10.1007/s002080200318",

language = "English",

volume = "323",

pages = "609--623",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - The local root number of elliptic curves with wild ramification

AU - Kobayashi, Shinichi

PY - 2002/12/1

Y1 - 2002/12/1

N2 - Let E be an elliptic curve over a number field F. The root number is conjecturally the sign of the functional equation of L-function of E/F. It is defined as the product of local signs over all places of F. The purpose of this paper is to describe this local sign by the coefficients of a Weierstraß equation of E.

AB - Let E be an elliptic curve over a number field F. The root number is conjecturally the sign of the functional equation of L-function of E/F. It is defined as the product of local signs over all places of F. The purpose of this paper is to describe this local sign by the coefficients of a Weierstraß equation of E.

UR - http://www.scopus.com/inward/record.url?scp=0036022793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036022793&partnerID=8YFLogxK

U2 - 10.1007/s002080200318

DO - 10.1007/s002080200318

M3 - Article

AN - SCOPUS:0036022793

SN - 0025-5831

VL - 323

SP - 609

EP - 623

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3

ER -

The local root number of elliptic curves with wild ramification

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this