With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical t- orems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s)=1. In the 1950's, a new theme was introduced by Birch and Swinnerton-Dyer. Given an elliptic curve E over a number ?eld K of ?nite degree over Q,they associated an L-function to E and conjectured that this L-function extends to an entire function and has a zero at s = 1 of order equal to the Z-rank of the group of K-rational points of E. In particular, the L-function vanishes at s=1ifand only if E has in?nitely many K-rational points.
With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical t- orems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s)=1. In the 1950's, a new theme was introduced by Birch and Swinnerton-Dyer. Given an elliptic curve E over a number ?eld K of ?nite degree over Q,they associated an L-function to E and conjectured that this L-function extends to an entire function and has a zero at s = 1 of order equal to the Z-rank of the group of K-rational points of E. In particular, the L-function vanishes at s=1ifand only if E has in?nitely many K-rational points.
- ISBN:
- 9783034802734
- 9783034802734
- Category:
- Number theory
- Format:
- Paperback
- Publication Date:
- 05-01-2012
- Language:
- English
- Publisher:
- Birkhauser Verlag AG
- Country of origin:
- Switzerland
- Pages:
- 196
- Dimensions (mm):
- 235x155x11mm
- Weight:
- 0.45kg
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