TY - JOUR
T1 - Fourier expansion of Arakawa lifting I
T2 - An explicit formula and examples of non-vanishing lifts
AU - Murase, Atsushi
AU - Narita, Hiroaki
N1 - Funding Information:
∗ Partially supported by Grand-in-Aid for Scientific Research C-20540031, JSPS. ∗∗ Partially supported by Grand-in-Aid for Young Scientists (B) 18749008, JSPS. Received June 15, 2009
Publisher Copyright:
© 2012, Springer New York LLC. All rights reserved.
PY - 2012/1/1
Y1 - 2012/1/1
N2 - Given an elliptic cusp form f and an automorphic form f′ on a definite quaternion algebra over ℚ, there is a theta lifting from (f, f′) to an automorphic form L(f, f′) on the quaternion unitary group GSp(1, 1) generating quaternionic discrete series at the Archimedean place. The aim of this paper is to provide an explicit formula for Fourier coefficients of L(f, f′) in terms of periods of f and f′ with respect to a unitary character χ of an imaginary quadratic field. As an application, we show the existence of (f, f′) with L(f, f′) ≠ 0.
AB - Given an elliptic cusp form f and an automorphic form f′ on a definite quaternion algebra over ℚ, there is a theta lifting from (f, f′) to an automorphic form L(f, f′) on the quaternion unitary group GSp(1, 1) generating quaternionic discrete series at the Archimedean place. The aim of this paper is to provide an explicit formula for Fourier coefficients of L(f, f′) in terms of periods of f and f′ with respect to a unitary character χ of an imaginary quadratic field. As an application, we show the existence of (f, f′) with L(f, f′) ≠ 0.
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U2 - 10.1007/s11856-011-0084-7
DO - 10.1007/s11856-011-0084-7
M3 - Article
AN - SCOPUS:79955888481
SN - 0021-2172
VL - 187
SP - 317
EP - 369
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -