"L-values of elliptic curves"의 두 판 사이의 차이
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imported>Pythagoras0 (새 문서: ==related items== * Mahler measures and L-values of elliptic curves ==articles== * '''[Z2013]''' Zudilin, Wadim. 2013. “Period(d)ness of L-Values.” In Number Theory and Rela...) |
imported>Pythagoras0 |
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| + | ==introduction== | ||
| + | * Computing $L(E;1)$ is easy: it is either 0 or the period of elliptic curve $E$ | ||
| + | * Computing $L(E;k)$ for $k\geq 2$ is highly non-trivial. The already mentioned results of Beilinson generalised later by Denninger-Scholl show that any such L-value can be expressed as a period. | ||
| + | * Several examples are explicitly given for $k=2$, mainly motivated by showing particular cases of Beilinson's conjectures in K-theory and Boyd's (conjectural) evaluations of Mahler measures. | ||
| + | * In spite of the algorithmic nature of Beilinson's method and in view of its complexity, no examples were produced so far for a single $L(E;3)$. | ||
| + | * Rogers and Zudilin in 2010-11 created an elementary alternative to Beilinson-Denninger-Scholl to prove some conjectural Mahler evaluations. | ||
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| + | |||
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==related items== | ==related items== | ||
* [[Mahler measures and L-values of elliptic curves]] | * [[Mahler measures and L-values of elliptic curves]] | ||
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| + | ==expositions== | ||
| + | * Zudilin, Wadim [http://carma.newcastle.edu.au/wadim/PS/NewDelhi-slides.pdf Hypergeometric evaluations of L-values of an elliptic curve] | ||
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2015년 1월 2일 (금) 02:47 판
introduction
- Computing $L(E;1)$ is easy: it is either 0 or the period of elliptic curve $E$
- Computing $L(E;k)$ for $k\geq 2$ is highly non-trivial. The already mentioned results of Beilinson generalised later by Denninger-Scholl show that any such L-value can be expressed as a period.
- Several examples are explicitly given for $k=2$, mainly motivated by showing particular cases of Beilinson's conjectures in K-theory and Boyd's (conjectural) evaluations of Mahler measures.
- In spite of the algorithmic nature of Beilinson's method and in view of its complexity, no examples were produced so far for a single $L(E;3)$.
- Rogers and Zudilin in 2010-11 created an elementary alternative to Beilinson-Denninger-Scholl to prove some conjectural Mahler evaluations.
expositions
- Zudilin, Wadim Hypergeometric evaluations of L-values of an elliptic curve
articles
- [Z2013] Zudilin, Wadim. 2013. “Period(d)ness of L-Values.” In Number Theory and Related Fields, edited by Jonathan M. Borwein, Igor Shparlinski, and Wadim Zudilin, 381–395. Springer Proceedings in Mathematics & Statistics 43. Springer New York. http://link.springer.com/chapter/10.1007/978-1-4614-6642-0_20.