Abstract
In this paper, we obtain a second term identity of the regularized Siegel–Weil formula for the unitary dual pair ( U ( 1 , 1 ) , U ( 1 , 1 ) ) , and we use this to derive a Rallis inner product formula for theta lifting from U ( 1 ) to U ( 1 , 1 ) . By choosing a good Schwartz function in the inner product formula, we obtain a special value formula for some Hecke L-function at s = 1 in terms of the norm of a theta function on U ( 1 , 1 ) .
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