Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse conjectured that this product has a meromorphic continuation over the whole plane and a functional equation.
Hasse's Conjecture
See also
Meromorphic Function, Prime IdealExplore with Wolfram|Alpha
References
Lang, S. "Some History of the Shimura-Taniyama Conjecture." Not. Amer. Math. Soc. 42, 1301-1307, 1995.Referenced on Wolfram|Alpha
Hasse's ConjectureCite this as:
Weisstein, Eric W. "Hasse's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HassesConjecture.html