On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials

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On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials. / Nordentoft, Asbjorn Christian.

In: International Mathematics Research Notices, Vol. 2021, No. 3, 2021, p. 1980-2006.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Nordentoft, AC 2021, 'On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials', International Mathematics Research Notices, vol. 2021, no. 3, pp. 1980-2006. https://doi.org/10.1093/imrn/rnaa194

APA

Nordentoft, A. C. (2021). On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials. International Mathematics Research Notices, 2021(3), 1980-2006. https://doi.org/10.1093/imrn/rnaa194

Vancouver

Nordentoft AC. On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials. International Mathematics Research Notices. 2021;2021(3):1980-2006. https://doi.org/10.1093/imrn/rnaa194

Author

Nordentoft, Asbjorn Christian. / On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials. In: International Mathematics Research Notices. 2021 ; Vol. 2021, No. 3. pp. 1980-2006.

Bibtex

@article{b592d865df5f4c86ae88d39470db7b4e,
title = "On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials",
abstract = "In this paper, we determine the limiting distribution of the image of the Eichler–Shimura map or equivalently the limiting joint distribution of the coefficients of the period polynomials associated to a fixed cusp form. The limiting distribution is shown to be the distribution of a certain transformation of two independent random variables both of which are equidistributed on the circle R/Z⁠, where the transformation is connected to the additive twist of the cuspidal L-function. Furthermore, we determine the asymptotic behavior of the zeroes of the period polynomials of a fixed cusp form. We use the method of moments and the main ingredients in the proofs are additive twists of L-functions and bounds for both individual and sums of",
author = "Nordentoft, {Asbjorn Christian}",
year = "2021",
doi = "10.1093/imrn/rnaa194",
language = "English",
volume = "2021",
pages = "1980--2006",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "3",

}

RIS

TY - JOUR

T1 - On the Distribution of Periods of Holomorphic Cusp Forms and Zeroes of Period Polynomials

AU - Nordentoft, Asbjorn Christian

PY - 2021

Y1 - 2021

N2 - In this paper, we determine the limiting distribution of the image of the Eichler–Shimura map or equivalently the limiting joint distribution of the coefficients of the period polynomials associated to a fixed cusp form. The limiting distribution is shown to be the distribution of a certain transformation of two independent random variables both of which are equidistributed on the circle R/Z⁠, where the transformation is connected to the additive twist of the cuspidal L-function. Furthermore, we determine the asymptotic behavior of the zeroes of the period polynomials of a fixed cusp form. We use the method of moments and the main ingredients in the proofs are additive twists of L-functions and bounds for both individual and sums of

AB - In this paper, we determine the limiting distribution of the image of the Eichler–Shimura map or equivalently the limiting joint distribution of the coefficients of the period polynomials associated to a fixed cusp form. The limiting distribution is shown to be the distribution of a certain transformation of two independent random variables both of which are equidistributed on the circle R/Z⁠, where the transformation is connected to the additive twist of the cuspidal L-function. Furthermore, we determine the asymptotic behavior of the zeroes of the period polynomials of a fixed cusp form. We use the method of moments and the main ingredients in the proofs are additive twists of L-functions and bounds for both individual and sums of

U2 - 10.1093/imrn/rnaa194

DO - 10.1093/imrn/rnaa194

M3 - Journal article

VL - 2021

SP - 1980

EP - 2006

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 3

ER -

ID: 284408818