TY - JOUR
T1 - Arithmetic theta lifting and L-derivatives for unitary groups, II
AU - Liu, Yifeng
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2011
Y1 - 2011
N2 - We prove the arithmetic inner product formula conjectured in the first paper of this series for n = 1, that is, for the group U(1,1)F unconditionally. The formula relates central L-derivatives of weight-2 holomorphic cuspidal automorphic representations of U(1,1)F with ε-factor -1 with the Néron-Tate height pairing of special cycles on Shimura curves of unitary groups. In particular, we treat all kinds of ramification in a uniform way. This generalizes the arithmetic inner product formula obtained by Kudla, Rapoport, and Yang, which holds for certain cusp eigenforms of PGL(2)Q of square-free level.
AB - We prove the arithmetic inner product formula conjectured in the first paper of this series for n = 1, that is, for the group U(1,1)F unconditionally. The formula relates central L-derivatives of weight-2 holomorphic cuspidal automorphic representations of U(1,1)F with ε-factor -1 with the Néron-Tate height pairing of special cycles on Shimura curves of unitary groups. In particular, we treat all kinds of ramification in a uniform way. This generalizes the arithmetic inner product formula obtained by Kudla, Rapoport, and Yang, which holds for certain cusp eigenforms of PGL(2)Q of square-free level.
KW - Arithmetic inner product formula
KW - Arithmetic theta lifting
KW - L-derivatives
KW - Unitary Shimura curves
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U2 - 10.2140/ant.2011.5.923
DO - 10.2140/ant.2011.5.923
M3 - Article
AN - SCOPUS:84860013106
VL - 5
SP - 923
EP - 1000
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 6
ER -