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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.
References
Lang, S. ``Some History of the Shimura-Taniyama Conjecture.'' Not. Amer. Math. Soc. 42, 1301-1307, 1995.