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General multiple Dirichlet series from perverse sheaves - MaRDI portal

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General multiple Dirichlet series from perverse sheaves

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Publication:6508060

arXiv2209.13072MaRDI QIDQ6508060

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Abstract: We give an axiomatic characterization of multiple Dirichlet series over the function field mathbbFq(T), generalizing a set of axioms given by Diaconu and Pasol. The key axiom, relating the coefficients at prime powers to sums of the coefficients, formalizes an observation of Chinta. The existence of multiple Dirichlet series satisfying these axioms is proved by exhibiting the coefficients as trace functions of explicit perverse sheaves, and using properties of perverse sheaves. The multiple Dirichlet series defined this way include, as a special case, many that have appeared previously in the literature.












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