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Difference equations over fields of elliptic functions. Deshalit, Ehud
Description
Adamczewski and Bell proved in 2017 a 30-year old conjecture of Loxton and van der Poorten, asserting that a Laurent power series, which simultaneously satisfies a p-Mahler equation and a q-Mahler equation for multiplicatively independent integers p and q, is a rational function. Similar looking theorems have been proved by Bezivin-Boutabaa and Ramis for pairs of difference, or difference-differential equations. Recently, Schafke and Singer gave a unified treatment of all these theorems. In this talk we shall discuss a similar theorem for (p,q)-difference equations over fields of elliptic functions. Despite having the same flavor, there are substantial differences, having to do with issues of periodicity, and with the existence of non-trivial (p,q)-invariant vector bundles on the elliptic curve.
Item Metadata
Title |
Difference equations over fields of elliptic functions.
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-11-09T09:59
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Description |
Adamczewski and Bell proved in 2017 a 30-year old conjecture of Loxton
and van der Poorten, asserting that a Laurent power series, which simultaneously
satisfies a p-Mahler equation and a q-Mahler equation for multiplicatively independent
integers p and q, is a rational function. Similar looking theorems have been proved by
Bezivin-Boutabaa and Ramis for pairs of difference, or difference-differential equations.
Recently, Schafke and Singer gave a unified treatment of all these theorems.
In this talk we shall discuss a similar theorem for (p,q)-difference equations over fields of
elliptic functions. Despite having the same flavor, there are substantial differences, having
to do with issues of periodicity, and with the existence of non-trivial (p,q)-invariant vector
bundles on the elliptic curve.
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Extent |
60.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Hebrew University of Jerusalem
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Series | |
Date Available |
2021-05-09
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0397353
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International