Preprint: Twisting moduli for gl(2)
Bedert, B., Cooper, G., Oliver, T. and Zhang, P. 2020. Preprint: Twisting moduli for gl(2). arXiv. https://doi.org/10.48550/arxiv.2003.02557
Bedert, B., Cooper, G., Oliver, T. and Zhang, P. 2020. Preprint: Twisting moduli for gl(2). arXiv. https://doi.org/10.48550/arxiv.2003.02557
| Title | Preprint: Twisting moduli for gl(2) |
|---|---|
| Authors | Bedert, B., Cooper, G., Oliver, T. and Zhang, P. |
| Description | We prove various converse theorems for automorphic forms on \Gamma_0(N), each assuming fewer twisted functional equations than the last. We show that no twisting at all is needed for holomorphic modular forms in the case that N is 18, 20, or 24 - these integers are the smallest multiples of 4 or 9 not covered by earlier work of Conrey-Farmer. This development is a consequence of finding generating sets for \Gamma_0(N) such that each generator can be written as a product of special matrices. As for real-analytic Maass forms of even (resp. odd) weight we prove the analogous statement for N=1,...12,16,18 (resp. N=1,...,12,14,15,16,17,18,20,23,24). |
| Year | 2020 |
| Output media | arXiv preprint |
| Publisher | arXiv |
| Publication dates | |
| Published | 05 Mar 2020 |
| ISSN | 2331-8422 |
| Digital Object Identifier (DOI) | https://doi.org/10.48550/arxiv.2003.02557 |
| Journal | ARXIV |
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Preprint: Machine Learning Class Numbers of Real Quadratic Fields
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Preprint: Machine-Learning the Sato-Tate Conjecture
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Preprint: Machine-learning number fields
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Preprint: Machine-learning arithmetic curves
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Twisting moduli for GL(2)
Bedert, B., Cooper, G., Oliver, T. and Zhang, P. 2020. Twisting moduli for GL(2). Journal of Number Theory. 217, pp. 142-162. https://doi.org/10.1016/j.jnt.2020.04.008
Weil's converse theorem for Maass forms and cancellation of zeros
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Preprint: Ratios of Artin L-functions
Hochfilzer, L. and Oliver, T. 2019. Preprint: Ratios of Artin L-functions. arXiv. https://doi.org/10.48550/arxiv.1910.02821
Preprint: Weil's Converse Theorem for Maass Forms and Cancellation of Zeros
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A conjectural extension of Hecke’s converse theorem
Bettin, S., Bober, J., Booker, A., Conrey, B., Lee, M., Molteni, G., Oliver, T., Platt, D. and Steiner, R. 2018. A conjectural extension of Hecke’s converse theorem. The Ramanujan Journal. 47, pp. 659-684. https://doi.org/10.1007/s11139-017-9953-y
A conjectural extension of hecke's converse theorem
Bettin, S., Bober, J.W., Booker, A.R., Conrey, B., Lee, M., Molteni, G., Oliver, T., Platt, D.J. and Steiner, R.S. 2017. A conjectural extension of hecke's converse theorem. arXiv. https://doi.org/10.48550/arxiv.1704.02570
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Zeta integrals on arithmetic surfaces
Oliver, T. 2016. Zeta integrals on arithmetic surfaces. St Petersburg Math. J.. 27, pp. 1003-1028. https://doi.org/10.1090/spmj/1432
Higher Dimensional Adeles, Mean-Periodicity and Zeta Functions of Arithmetic Surfaces
Oliver, T. 2014. Higher Dimensional Adeles, Mean-Periodicity and Zeta Functions of Arithmetic Surfaces. PhD thesis University of Nottingham School of Mathematical Sciences
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