Pole Structure of Shintani zeta functions and Newton Polytopes.

Diego Lopez Valenci (U of Potsdam)

Nov 12. 2021, 14:15 — 14:40

Shintani zeta functions are a generalization of multiple zeta functions and conical zeta functions. It is known that they extend to meromorphic functions with poles in affine hyperplanes. In this talk I will present a refinement of the known result showing that the poles lie on hyperplanes parallel to the facets of certain convex polytopes associated to the defining matrix for the Shintani zeta function. Explicitly, the latter are the Newton polytopes of the polynomials induced by the columns of the underlying matrix. This work is part of my PhD.


Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation (Graduate School)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)