Booher, JeremyVoloch, Jose2021-10-312021-10-312020Booher J, Voloch JF (2020). Recovering algebraic curves from L-functions of Hilbert class fields. Research in Number Theory. 6(4).2522-01602363-9555https://hdl.handle.net/10092/102799In this paper, we prove that a smooth hyperbolic projective curve over a finite field can be recovered from L-functions associated to the Hilbert class field of the curve and its constant field extensions. As a consequence, we give a new proof of a result of Mochizuki and Tamagawa that two such curves with isomorphic fundamental groups are themselves isomorphic.enAll rights reserved unless otherwise statedmath.NTmath.AG11G20Journal Article2021-07-16Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theoryFields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490402 - Algebraic and differential geometryhttp://doi.org/10.1007/s40993-020-00222-0