Editing Hasse–Weil zeta function (section)

==Hasse–Weil conjecture==

The Hasse–Weil conjecture states that the Hasse–Weil zeta function should extend to a meromorphic function for all complex ''s'', and should satisfy a functional equation similar to that of the [[Riemann zeta function]]. For elliptic curves over the rational numbers, the Hasse–Weil conjecture follows<ref name="ThesisProblem">{{cite journal | last=Milne | first=James S. | title=The Riemann hypothesis over finite fields: from Weil to the present day | journal=Notices of the International Congress of Chinese Mathematicians | volume=4 | issue=2 | date=2016 | doi=10.4310/ICCM.2016.v4.n2.a4 | doi-access=free | pages=14–52| arxiv=1509.00797 }}</ref> from the [[modularity theorem]]: each elliptic curve {{mvar|E}} over <math>\Q</math> is modular.