General multiple Dirichlet series from perverse sheaves

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We give an axiomatic characterization of multiple Dirichlet series over the function field Fq(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 special cases, many that have appeared previously in the literature.

Original languageEnglish (US)
Pages (from-to)408-453
Number of pages46
JournalJournal of Number Theory
StatePublished - Sep 2024

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Dirichlet series
  • Finite fields
  • Function fields
  • Intersection cohomology
  • Multiple Dirichlet series
  • Perverse sheaves
  • Polynomials
  • Twisted multiplicativity


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