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Generators for the group of modular units for $\Gamma^1(N)$ over the rationals
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Authors : Streng, Marco (Author of the conference)
CIRM (Publisher )
11B37 - Recurrences [For applications to special functions, see 33-XX]
11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
11F03 - Modular and automorphic functions
11G16 - Elliptic and modular units [See also 11R27]
14H52 - Elliptic curves
CIRM (Publisher )
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Abstract :
The modular curve $Y^1(N)$ parametrises pairs $(E,P)$, where $E$ is an elliptic curve and $P$ is a point of order $N$ on $E$, up to isomorphism. A unit on the affine curve $Y^1(N)$ is a holomorphic function that is nowhere zero and I will mention some applications of the group of units in the talk.
The main result is a way of generating generators (sic) of this group using a recurrence relation. The generators are essentially the defining equations of $Y^1(N)$ for $n < (N + 3)/2$. This result proves a conjecture of Maarten Derickx and Mark van Hoeij.
MSC Codes : The main result is a way of generating generators (sic) of this group using a recurrence relation. The generators are essentially the defining equations of $Y^1(N)$ for $n < (N + 3)/2$. This result proves a conjecture of Maarten Derickx and Mark van Hoeij.
11B37 - Recurrences [For applications to special functions, see 33-XX]
11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
11F03 - Modular and automorphic functions
11G16 - Elliptic and modular units [See also 11R27]
14H52 - Elliptic curves
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/06/2015 Conference Date : 18/05/2015 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry Mathematical Area(s) : Number Theory ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:27:47 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-05-18_Streng.mp4 
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Information on the Event
Event Title : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codesEvent Organizers : Bassa, Alp ; Couvreur, Alain ; Kohel, David Dates : 18/05/15 - 22/05/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1193.html
Citation Data
DOI : 10.24350/CIRM.V.18766003Cite this video as: Streng, Marco (2015). Generators for the group of modular units for $\Gamma^1(N)$ over the rationals. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18766003 URI : http://dx.doi.org/10.24350/CIRM.V.18766003 |
Bibliography
- Streng, M. (2015). Generators of the group of modular units for $\Gamma^1(N)$ over $\mathbf{Q}$.
