The Growth of CM Periods over False Tate Extensions

D Delbourgo; T Ward

doi:10.1080/10586458.2010.10129075

The Growth of CM Periods over False Tate Extensions

D Delbourgo, T Ward

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

10 Citations (Scopus)

Abstract

We prove weak forms of Kato's K1-congruences for elliptic curves with complex multiplication, subject to two technical hypotheses. We next use MAGMA to calculate the µ-invariant measuring the discrepancy between the "motivic" and "automorphic" p-adic L-functions. Via the two-variable main conjecture, one can then estimate growth in this µ-invariant using arithmetic of the 2 p -extension.

Translated title of the contribution	The Growth of CM Periods over False Tate Extensions
Original language	English
Pages (from-to)	195 - 210
Number of pages	16
Journal	Experimental Mathematics
Volume	19, issue 2
DOIs	https://doi.org/10.1080/10586458.2010.10129075
Publication status	Published - Apr 2010

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Publisher: Taylor & Francis

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10.1080/10586458.2010.10129075

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title = "The Growth of CM Periods over False Tate Extensions",

abstract = "We prove weak forms of Kato's K1-congruences for elliptic curves with complex multiplication, subject to two technical hypotheses. We next use MAGMA to calculate the µ-invariant measuring the discrepancy between the {"}motivic{"} and {"}automorphic{"} p-adic L-functions. Via the two-variable main conjecture, one can then estimate growth in this µ-invariant using arithmetic of the 2 p -extension.",

author = "D Delbourgo and T Ward",

note = "Publisher: Taylor & Francis",

year = "2010",

month = apr,

doi = "10.1080/10586458.2010.10129075",

language = "English",

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T1 - The Growth of CM Periods over False Tate Extensions

AU - Delbourgo, D

AU - Ward, T

N1 - Publisher: Taylor & Francis

PY - 2010/4

Y1 - 2010/4

N2 - We prove weak forms of Kato's K1-congruences for elliptic curves with complex multiplication, subject to two technical hypotheses. We next use MAGMA to calculate the µ-invariant measuring the discrepancy between the "motivic" and "automorphic" p-adic L-functions. Via the two-variable main conjecture, one can then estimate growth in this µ-invariant using arithmetic of the 2 p -extension.

AB - We prove weak forms of Kato's K1-congruences for elliptic curves with complex multiplication, subject to two technical hypotheses. We next use MAGMA to calculate the µ-invariant measuring the discrepancy between the "motivic" and "automorphic" p-adic L-functions. Via the two-variable main conjecture, one can then estimate growth in this µ-invariant using arithmetic of the 2 p -extension.

U2 - 10.1080/10586458.2010.10129075

DO - 10.1080/10586458.2010.10129075

M3 - Article (Academic Journal)

SN - 1058-6458

VL - 19, issue 2

SP - 195

EP - 210

JO - Experimental Mathematics

JF - Experimental Mathematics

ER -

The Growth of CM Periods over False Tate Extensions

Abstract

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