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We model the field $F_1$ of one element as a lambda ring $\bf Z$ with thecanonical lambda structure. We show that then we can calculate the Riemann zetafunction of integers in two ways: the first, geometrical, as a zeta function ofthe affine line over $F_1$ and the second, categorical, as a zeta function ofthe category of modules over $F_1$.

An approach to F_1 via the theory of lambda rings