Random matrix theory and moments of moments of $L$-functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909410924691456 |
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| author | Andrade, J. C. Best, C. G. |
| author_facet | Andrade, J. C. Best, C. G. |
| contents | We give an analytic proof of the asymptotic behaviour of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order coefficients previously found by Assiotis, Bailey and Keating. We also discuss the conjectures of Bailey and Keating for the corresponding moments of moments of L-functions with symplectic and orthogonal symmetry. Specifically, we show that these conjectures follow from the shifted moments conjecture of Conrey, Farmer, Keating, Rubinstein and Snaith. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07282 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Random matrix theory and moments of moments of $L$-functions Andrade, J. C. Best, C. G. Mathematical Physics Number Theory We give an analytic proof of the asymptotic behaviour of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order coefficients previously found by Assiotis, Bailey and Keating. We also discuss the conjectures of Bailey and Keating for the corresponding moments of moments of L-functions with symplectic and orthogonal symmetry. Specifically, we show that these conjectures follow from the shifted moments conjecture of Conrey, Farmer, Keating, Rubinstein and Snaith. |
| title | Random matrix theory and moments of moments of $L$-functions |
| topic | Mathematical Physics Number Theory |
| url | https://arxiv.org/abs/2205.07282 |