Non-vanishing of Taylor coefficients and Poincaré series

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Non-vanishing of Taylor coefficients and Poincaré series. / O'Sullivan, C.; Risager, Morten S.

In: Ramanujan Journal, Vol. 30, No. 1, 01.01.2013, p. 67-100.

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

Harvard

O'Sullivan, C & Risager, MS 2013, 'Non-vanishing of Taylor coefficients and Poincaré series', Ramanujan Journal, vol. 30, no. 1, pp. 67-100. https://doi.org/10.1007/s11139-012-9374-x

APA

O'Sullivan, C., & Risager, M. S. (2013). Non-vanishing of Taylor coefficients and Poincaré series. Ramanujan Journal, 30(1), 67-100. https://doi.org/10.1007/s11139-012-9374-x

Vancouver

O'Sullivan C, Risager MS. Non-vanishing of Taylor coefficients and Poincaré series. Ramanujan Journal. 2013 Jan 1;30(1):67-100. https://doi.org/10.1007/s11139-012-9374-x

Author

O'Sullivan, C. ; Risager, Morten S. / Non-vanishing of Taylor coefficients and Poincaré series. In: Ramanujan Journal. 2013 ; Vol. 30, No. 1. pp. 67-100.

Bibtex

@article{ab476d713a8f4edb82bf1347e33fff9f,
title = "Non-vanishing of Taylor coefficients and Poincar{\'e} series",
abstract = "We prove recursive formulas for the Taylor coefficients of cusp forms, such as Ramanujan's Delta function, at points in the upper half-plane. This allows us to show the non-vanishing of all Taylor coefficients of Delta at CM points of small discriminant as well as the non-vanishing of certain Poincar{\'e} series. At a {"}generic{"} point, all Taylor coefficients are shown to be non-zero. Some conjectures on the Taylor coefficients of Delta at CM points are stated.",
author = "C. O'Sullivan and Risager, {Morten S.}",
year = "2013",
month = jan,
day = "1",
doi = "10.1007/s11139-012-9374-x",
language = "English",
volume = "30",
pages = "67--100",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Non-vanishing of Taylor coefficients and Poincaré series

AU - O'Sullivan, C.

AU - Risager, Morten S.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We prove recursive formulas for the Taylor coefficients of cusp forms, such as Ramanujan's Delta function, at points in the upper half-plane. This allows us to show the non-vanishing of all Taylor coefficients of Delta at CM points of small discriminant as well as the non-vanishing of certain Poincaré series. At a "generic" point, all Taylor coefficients are shown to be non-zero. Some conjectures on the Taylor coefficients of Delta at CM points are stated.

AB - We prove recursive formulas for the Taylor coefficients of cusp forms, such as Ramanujan's Delta function, at points in the upper half-plane. This allows us to show the non-vanishing of all Taylor coefficients of Delta at CM points of small discriminant as well as the non-vanishing of certain Poincaré series. At a "generic" point, all Taylor coefficients are shown to be non-zero. Some conjectures on the Taylor coefficients of Delta at CM points are stated.

UR - http://www.scopus.com/inward/record.url?scp=84872488395&partnerID=8YFLogxK

U2 - 10.1007/s11139-012-9374-x

DO - 10.1007/s11139-012-9374-x

M3 - Journal article

AN - SCOPUS:84872488395

VL - 30

SP - 67

EP - 100

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 1

ER -

ID: 98447949