Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916117937651712 |
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| author | Bergström, Jonas Diaconu, Adrian Petersen, Dan Westerland, Craig |
| author_facet | Bergström, Jonas Diaconu, Adrian Petersen, Dan Westerland, Craig |
| contents | We compute the stable homology of the braid group with coefficients in any Schur functor applied to the integral reduced Burau representation. This may be considered as a hyperelliptic analogue of the Mumford conjecture (Madsen--Weiss theorem) with twisted coefficients. We relate the result to the function field case of conjectures of Conrey-Farmer-Keating-Rubinstein-Snaith on moments of families of quadratic $L$-functions. Combined with a recent homological stability theorem of Miller-Patzt-Petersen-Randal-Williams, our homological calculations confirm the Conrey-Farmer-Keating-Rubinstein-Snaith predictions for all large enough prime powers $q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07664 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions Bergström, Jonas Diaconu, Adrian Petersen, Dan Westerland, Craig Number Theory Algebraic Geometry Algebraic Topology Geometric Topology We compute the stable homology of the braid group with coefficients in any Schur functor applied to the integral reduced Burau representation. This may be considered as a hyperelliptic analogue of the Mumford conjecture (Madsen--Weiss theorem) with twisted coefficients. We relate the result to the function field case of conjectures of Conrey-Farmer-Keating-Rubinstein-Snaith on moments of families of quadratic $L$-functions. Combined with a recent homological stability theorem of Miller-Patzt-Petersen-Randal-Williams, our homological calculations confirm the Conrey-Farmer-Keating-Rubinstein-Snaith predictions for all large enough prime powers $q$. |
| title | Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions |
| topic | Number Theory Algebraic Geometry Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2302.07664 |