Non-vanishing of Taylor coefficients and Poincaré series
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
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
APA
Vancouver
Author
Bibtex
}
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