Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields
Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet L–functions over function fields. We denote the various terms arising as Type-0, Type-I and Type-II contributions. When the support of the Fourie...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2020
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| _version_ | 1826272155727298560 |
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| author | Bui, H Florea, A Keating, J |
| author_facet | Bui, H Florea, A Keating, J |
| author_sort | Bui, H |
| collection | OXFORD |
| description | Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet L–functions over function fields. We denote the various terms arising as Type-0, Type-I and Type-II contributions. When the support of the Fourier transform of the test function is sufficiently restricted, we rigorously compute the Type-0 and Type-I terms and confirm that they match the conjectured answer. When the restrictions on the support are relaxed, our results suggest that Type-II contributions become important in the two level density.
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| first_indexed | 2024-03-06T22:08:04Z |
| format | Journal article |
| id | oxford-uuid:50d79421-3556-4bbc-bed6-dace7d7bf5a2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:08:04Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:50d79421-3556-4bbc-bed6-dace7d7bf5a22022-03-26T16:16:06ZType-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fieldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:50d79421-3556-4bbc-bed6-dace7d7bf5a2EnglishSymplectic ElementsElsevier2020Bui, HFlorea, AKeating, JUsing the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet L–functions over function fields. We denote the various terms arising as Type-0, Type-I and Type-II contributions. When the support of the Fourier transform of the test function is sufficiently restricted, we rigorously compute the Type-0 and Type-I terms and confirm that they match the conjectured answer. When the restrictions on the support are relaxed, our results suggest that Type-II contributions become important in the two level density. |
| spellingShingle | Bui, H Florea, A Keating, J Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields |
| title | Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields |
| title_full | Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields |
| title_fullStr | Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields |
| title_full_unstemmed | Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields |
| title_short | Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields |
| title_sort | type i contributions to the one and two level densities of quadratic dirichlet l functions over function fields |
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