CRM: Centro De Giorgi
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Zeta functions and L-series in positive characteristic

26 November 2012 - 30 November 2012


Parallel to the theory of the classical zeta and L-series with values in the field of complex numbers, a younger theory of analogous functions but with values in function fields of positive characteristic provides suggestive analogies and intriguing problems. For example, Goss' zeta function is believed to be of the same nature as Riemann's zeta function. However, no known functional equation exist for it leaving certain analogies with Riemann's zeta function without satisfactory explanation. The aim of this workshop is to consolidate recent progress and to start new projects and collaborations by focusing on some of the most striking aspects and advances: functional equations, arithmetic of special values, BSD conjectures, Riemann's hypothesis, link with t-motives, cohomological techniques, Kummer-Vandiver, Mazur-Wiles etc.