Constantinescu, P;
(2020)
Distribution of Modular Symbols in ℍ3.
International Mathematics Research Notices
10.1093/imrn/rnaa241.
(In press).
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Abstract
We introduce a new technique for the study of the distribution of modular symbols, which we apply to the congruence subgroups of Bianchi groups. We prove that if K is a quadratic imaginary number field of class number one and OK is its ring of integers, then for certain congruence subgroups of PSL2(OK), the periods of a cusp form of weight two obey asymptotically a normal distribution. These results are specialisations from the more general setting of quotient surfaces of cofinite Kleinian groups where our methods apply. We avoid the method of moments. Our new insight is to use the behaviour of the smallest eigenvalue of the Laplacian for spaces twisted by modular symbols. Our approach also recovers the first and second moments of the distribution.
| Type: | Article |
|---|---|
| Title: | Distribution of Modular Symbols in ℍ3 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imrn/rnaa241 |
| Publisher version: | https://doi.org/10.1093/imrn/rnaa241 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10111305 |
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