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Blanco, Guillem
Advances in mathematics (New York. 1965), 07/2019, Letnik: 350Journal Article, Publication
We study the poles and residues of the complex zeta function fs of a plane curve. We prove that most non-rupture divisors do not contribute to poles of fs or roots of the Bernstein-Sato polynomial bf(s) of f. For plane branches we give an optimal set of candidates for the poles of fs from the rupture divisors and the characteristic sequence of f. We prove that for generic plane branches fgen all the candidates are poles of fgens. As a consequence, we prove Yano's conjecture for any number of characteristic exponents if the eigenvalues of the monodromy of f are different.
