General multiple Dirichlet series from perverse sheaves
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914750644879360 |
|---|---|
| author | Sawin, Will |
| author_facet | Sawin, Will |
| contents | We give an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb F_q(T)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13072 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | General multiple Dirichlet series from perverse sheaves Sawin, Will Number Theory Algebraic Geometry We give an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb F_q(T)$, 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. |
| title | General multiple Dirichlet series from perverse sheaves |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2209.13072 |