The Zeta Function and Weil Conjecture for Elliptic Curves
碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 107 === For this thesis, we will compute the zeta functions and prove the Weil Conjecture for the elliptic curves. While we compute the zeta functions of elliptic curves, it is important to determine the number of the points on E over F_{q^s} . We will show that the...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2019
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/ew2vku |
| Summary: | 碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 107 === For this thesis, we will compute the zeta functions and prove the Weil Conjecture for the elliptic curves.
While we compute the zeta functions of elliptic curves, it is important to determine the number of the points on E over F_{q^s} .
We will show that the degree of an endomorphism on E is equal to the number of its kernel. We consider the n-torsion subgroup, which is isomorphic to Zn ⊕ Zn. And we will show that det(α_n) ≡ deg(α) (mod n). Then we can determine the points on elliptic curves.
Finally, we will prove the Weil conjecture for elliptic curves, and show that Z(q^{−k}) can be defined in a similar way to the Riemann zeta function.
|
|---|