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Monodromy eigenvalues and poles of zeta functions
Author(s) -
Cauwbergs Thomas,
Veys Willem
Publication year - 2017
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12003
Subject(s) - monodromy , mathematics , eigenvalues and eigenvectors , riemann zeta function , arithmetic zeta function , polynomial , prime zeta function , pure mathematics , conjecture , differential (mechanical device) , mathematical analysis , function (biology) , physics , quantum mechanics , evolutionary biology , biology , thermodynamics
The monodromy conjecture predicts that the poles of the topological zeta function and related zeta functions associated to a polynomial f induce monodromy eigenvalues of f . However, not every monodromy eigenvalue can be recovered from a pole. More generally, one also considers zeta functions associated to a polynomial and a differential form. We attach to f a suitable class of differential forms, such that each pole of the topological zeta function of f and such a form induces a monodromy eigenvalue, and moreover such that all monodromy eigenvalues are obtained this way.