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math.NT2019
L-series and homomorphisms of number fields
Harry Smit
While the zeta function does not determine a number field uniquely, the -series of a well-chosen Dirichlet character does. Moreover, isomorphisms between two number fields are i…
math.NT2019
L-series and isogenies of abelian varieties
Harry Smit
Faltings's isogeny theorem states that two abelian varieties are isogenous over a number field precisely when the characteristic polynomials of the reductions at almost all prime i…
math.NT2019
L-series and isomorphisms of number fields
Harry Smit
Two number fields with equal Dedekind zeta function are not necessarily isomorphic. However, if the number fields have equal sets of Dirichlet -series then they \emph{are} isomo…