On the lifting of hermitian modular forms
2008 ◽
Vol 144
(5)
◽
pp. 1107-1154
◽
Keyword(s):
AbstractLet K be an imaginary quadratic field with discriminant −D. We denote by 𝒪 the ring of integers of K. Let χ be the primitive Dirichlet character corresponding to K/ℚ. Let $\Gamma ^{(m)}_K=\mathrm {U} (m,m)({\mathbb Q})\cap \mathrm {GL}_{2m}({\cal O})$ be the hermitian modular group of degree m. We construct a lifting from S2k(SL2(ℤ)) to S2k+2n(ΓK(2n+1),det −k−n) and a lifting from S2k+1(Γ0(D),χ) to S2k+2n(ΓK(2n),det −k−n). We give an explicit Fourier coefficient formula of the lifting. This is a generalization of the Maass lift considered by Kojima, Krieg and Sugano. We also discuss its extension to the adele group of U(m,m).
Keyword(s):
1991 ◽
Vol 34
(3)
◽
pp. 417-422
◽
Keyword(s):
2015 ◽
Vol 145
(6)
◽
pp. 1153-1182
◽
Keyword(s):
Keyword(s):
2004 ◽
Vol 2004
(45)
◽
pp. 2383-2400
2012 ◽
Vol 15
◽
pp. 113-139
◽
2015 ◽
Vol 151
(9)
◽
pp. 1585-1625
◽
2011 ◽
Vol 55
(1)
◽
pp. 167-179
◽