Averaging over Heegner Points in the Hyperbolic Circle Problem

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Standard

Averaging over Heegner Points in the Hyperbolic Circle Problem. / Petridis, Yiannis N.; Risager, Morten S.

I: International Mathematics Research Notices, Bind 2018, Nr. 16, 2018, s. 4942-4968.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Petridis, YN & Risager, MS 2018, 'Averaging over Heegner Points in the Hyperbolic Circle Problem', International Mathematics Research Notices, bind 2018, nr. 16, s. 4942-4968. https://doi.org/10.1093/imrn/rnx026

APA

Petridis, Y. N., & Risager, M. S. (2018). Averaging over Heegner Points in the Hyperbolic Circle Problem. International Mathematics Research Notices, 2018(16), 4942-4968. https://doi.org/10.1093/imrn/rnx026

Vancouver

Petridis YN, Risager MS. Averaging over Heegner Points in the Hyperbolic Circle Problem. International Mathematics Research Notices. 2018;2018(16):4942-4968. https://doi.org/10.1093/imrn/rnx026

Author

Petridis, Yiannis N. ; Risager, Morten S. / Averaging over Heegner Points in the Hyperbolic Circle Problem. I: International Mathematics Research Notices. 2018 ; Bind 2018, Nr. 16. s. 4942-4968.

Bibtex

@article{a404e04bde4848b8a33dc5fcb89b94a0,
title = "Averaging over Heegner Points in the Hyperbolic Circle Problem",
abstract = "For Gamma = PSL2(Z) the hyperbolic circle problem aims to estimate the number of elements of the orbit Gamma z inside the hyperbolic disc centred at z with radius cosh(-1) (X/2). We show that, by averaging over Heegner points z of discriminant D, Selberg's error term estimate can be improved, if D is large enough. The proof uses bounds on spectral exponential sums, and results towards the sup-norm conjecture of eigenfunctions, and the Lindelof conjecture for twists of the L-functions attached to Maass cusp forms.",
author = "Petridis, {Yiannis N.} and Risager, {Morten S.}",
year = "2018",
doi = "10.1093/imrn/rnx026",
language = "English",
volume = "2018",
pages = "4942--4968",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "16",

}

RIS

TY - JOUR

T1 - Averaging over Heegner Points in the Hyperbolic Circle Problem

AU - Petridis, Yiannis N.

AU - Risager, Morten S.

PY - 2018

Y1 - 2018

N2 - For Gamma = PSL2(Z) the hyperbolic circle problem aims to estimate the number of elements of the orbit Gamma z inside the hyperbolic disc centred at z with radius cosh(-1) (X/2). We show that, by averaging over Heegner points z of discriminant D, Selberg's error term estimate can be improved, if D is large enough. The proof uses bounds on spectral exponential sums, and results towards the sup-norm conjecture of eigenfunctions, and the Lindelof conjecture for twists of the L-functions attached to Maass cusp forms.

AB - For Gamma = PSL2(Z) the hyperbolic circle problem aims to estimate the number of elements of the orbit Gamma z inside the hyperbolic disc centred at z with radius cosh(-1) (X/2). We show that, by averaging over Heegner points z of discriminant D, Selberg's error term estimate can be improved, if D is large enough. The proof uses bounds on spectral exponential sums, and results towards the sup-norm conjecture of eigenfunctions, and the Lindelof conjecture for twists of the L-functions attached to Maass cusp forms.

U2 - 10.1093/imrn/rnx026

DO - 10.1093/imrn/rnx026

M3 - Journal article

VL - 2018

SP - 4942

EP - 4968

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 16

ER -

ID: 209574604