An elliptic curve has complex multiplication if its ring of endomorphisms is stricly larger than $\mathbb{Z}$, in this case special simmetry arises from the additional structure. In this thesis we will study these curves and we will prove for a subclass of such curves the Weil conjectures, the analytic continuation and the functional equation of the Hasse-Weil zeta function.
An elliptic curve has complex multiplication if its ring of endomorphisms is stricly larger than $\mathbb{Z}$, in this case special simmetry arises from the additional structure. In this thesis we will study these curves and we will prove for a subclass of such curves the Weil conjectures, the analytic continuation and the functional equation of the Hasse-Weil zeta function.
Elliptic Curves with Complex Multiplication
MARCHESINI, LUCA
2021/2022
Abstract
An elliptic curve has complex multiplication if its ring of endomorphisms is stricly larger than $\mathbb{Z}$, in this case special simmetry arises from the additional structure. In this thesis we will study these curves and we will prove for a subclass of such curves the Weil conjectures, the analytic continuation and the functional equation of the Hasse-Weil zeta function.| File | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/32715