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Working paper

On the monodromy conjecture for non-degenerate hypersurfaces

arxiv.org. math. Cornell University, 2016. No. arXiv:1309.0630v4.
Takeuchi K., Esterov A. I., Lemahieu A.
Recently the second author and Van Proeyen proved the monodromy conjecture on topological zeta functions for all non-degenerate surface singularities. In this paper, we obtain higher-dimensional analogues of their results, which, in particular, prove the conjecture for all isolated singularities of 4 variables, as well as for many classes of non-isolated and higher-dimensional singularities. One of the tools that we introduce is a certain extension of the notion of a supermodular function, which may be of independent interest in convex analysis and game theory.