Weil's converse theorem for Maass forms and cancellation of zeros : WestminsterResearch

Publication dates
Title	Weil's converse theorem for Maass forms and cancellation of zeros
Type	Journal article
Authors	Oliver, T. and Neururer, M.
Abstract	We prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened analytic assumption applies in the context of our second theorem, which shows that the quotient of the symmetric square L-function of a Maass newform and the Riemann zeta function has infinitely many poles.
Journal	Acta Arithmetica
Journal citation	196, pp. 387-422
ISSN	0065-1036
	1730-6264
Year	2020
Publisher	Insitute of Mathematics, Polish Academy of Sciences
Accepted author manuscript	Accepted-converse-cancellation.pdf License CC BY 4.0 File Access Level Open (open metadata and files)
Digital Object Identifier (DOI)	https://doi.org/10.4064/aa190811-3-2
Web address (URL)	https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/196/4/113726/weil-s-converse-theorem-for-maass-forms-and-cancellation-of-zeros
Published online	11 Jul 2020

Related outputs

Murmurations of elliptic curves
Oliver, T., He, Y.-H., Lee, K.-H. and Pozdnyakov, A. 2024. Murmurations of elliptic curves. Experimental Mathematics. Advanced online publication. https://doi.org/10.1080/10586458.2024.2382361

Machine learning for number theory: unsupervised learning with L-functions
Oliver, T. 2024. Machine learning for number theory: unsupervised learning with L-functions. 8th International Congress on Mathematical Software (ICMS2024). Durham University 22 - 25 Jul 2024 Springer. https://doi.org/10.1007/978-3-031-64529-7_21

PCA, arithmetic, and murmurations
Oliver, T. 2024. PCA, arithmetic, and murmurations. Murmurations in Arithmetic. ICERM (Brown University) 06 - 08 Jul 2023 World Scientific Publishing. https://doi.org/10.1142/S2810939224400021

Preprint: Murmurations of Dirichlet Characters
Lee, K.-H., Oliver, T. and Pozdnyakov, A. 2023. Preprint: Murmurations of Dirichlet Characters. arXiv. https://doi.org/10.48550/arXiv.2307.00256

Machine Learning Class Numbers of Real Quadratic Fields
Oliver, T., Amir, M., He, Y.-H., Lee, K.-H. and Sultanow, E. 2023. Machine Learning Class Numbers of Real Quadratic Fields. International Journal of Data Science in the Mathematical Sciences. 1 (2), pp. 107-134. https://doi.org/10.1142/s2810939223500016

Counting points on elliptic curves
Oliver, T. and Wuthrich, C. 2023. Counting points on elliptic curves. LMS newsletter. 509, pp. 31-35. https://doi.org/10.1112/NLMS

Supervised learning of arithmetic invariants
Oliver, T. 2023. Supervised learning of arithmetic invariants. in: Yang-Hui He (ed.) Machine Learning in Pure Mathematics and Theoretical Physics World Scientific Publishing. pp. 331-363

Machine learning invariants of arithmetic curves
He, Y.-H., Lee, K.-H. and Oliver, T. 2023. Machine learning invariants of arithmetic curves. Journal of Symbolic Computation. 115, pp. 478-491. https://doi.org/10.1016/j.jsc.2022.08.017

Ratios of Artin L-functions
Hochfilzer, L. and Oliver, T. 2022. Ratios of Artin L-functions. Journal of Number Theory. 236, pp. 1-40. https://doi.org/10.1016/j.jnt.2021.07.007

Preprint: Murmurations of Elliptic Curves
He, Y.-H., Lee, K.-H., Oliver, T. and Pozdnyakov, A. 2022. Preprint: Murmurations of Elliptic Curves. arXiv. https://doi.org/10.48550/arxiv.2204.10140

Preprint: Machine Learning Class Numbers of Real Quadratic Fields
Amir, M., He, Y.-H., Lee, K.-H., Oliver, T. and Sultanow, E. 2022. Preprint: Machine Learning Class Numbers of Real Quadratic Fields. arXiv. https://doi.org/10.48550/arxiv.2209.09283

Preprint: Convergance of Kac-Moody Eisenstein Series over a Function Field
Lee, K.-H., Liu, D. and Oliver, T. 2022. Preprint: Convergance of Kac-Moody Eisenstein Series over a Function Field. arXiv. https://doi.org/10.48550/arxiv.2203.08628

Machine-learning the Sato-Tate conjecture
He, Y.-H., Lee, K.-H. and Oliver, T. 2022. Machine-learning the Sato-Tate conjecture. Journal of Symbolic Computation. 111, pp. 61-72. https://doi.org/10.1016/j.jsc.2021.11.002

Ratios of Artin L-functions
Hochfilzer, L. and Oliver, T. 2022. Ratios of Artin L-functions. Journal of Number Theory. 236, pp. 1-40. https://doi.org/10.1016/j.jnt.2021.07.007

Machine-learning number fields
He, Y.-H., Lee, K.-H. and Oliver, T. 2022. Machine-learning number fields. Mathematics, Computation and Geometry of Data. 2 (1), pp. 49-66. https://doi.org/10.4310/MCGD.2022.v2.n1.a2

Character expansion of Kac–Moody correction factors
Lee, K.-H., Liu, D and Oliver, T. 2021. Character expansion of Kac–Moody correction factors. Pacific Journal of Mathematics. 313 (1), pp. 159-183. https://doi.org/10.2140/pjm.2021.313.159

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

Preprint: Machine-Learning the Sato-Tate Conjecture
He, Y.-H., Lee, K.-H. and Oliver, T. 2020. Preprint: Machine-Learning the Sato-Tate Conjecture. arXiv. https://doi.org/10.48550/arxiv.2010.01213

Preprint: Machine-learning number fields
He, Y.-H., Lee, K.-H. and Oliver, T. 2020. Preprint: Machine-learning number fields. arXiv. https://doi.org/10.48550/arxiv.2011.08958

Preprint: Machine-learning arithmetic curves
He, Y.-H., Lee, K.-H. and Oliver, T. 2020. Preprint: Machine-learning arithmetic curves. arXiv. https://doi.org/10.48550/arxiv.2012.04084

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

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
Neururer, M. and Oliver, T. 2018. Preprint: Weil's Converse Theorem for Maass Forms and Cancellation of Zeros. arXiv. https://doi.org/10.48550/arxiv.1809.06586

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

Notes on low degree L-data
Oliver, T. 2017. Notes on low degree L-data. Analytic Number Theory and Related Areas. Research Institute for Mathematical Sciences, Kyoto University 04 - 06 Nov 2015

Automorphicity and mean-periodicity
Oliver, T. 2017. Automorphicity and mean-periodicity. Journal of the Mathematical Society of Japan. 69 (1), pp. 25-51. https://doi.org/10.2969/jmsj/06910025

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

Permalink - https://westminsterresearch.westminster.ac.uk/item/w4q45/weil-s-converse-theorem-for-maass-forms-and-cancellation-of-zeros

Weil's converse theorem for Maass forms and cancellation of zeros

Related outputs

Share this

Usage statistics

Export as