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TWISTED TRIPLE PRODUCT
$\text{p}$-ADIC L-FUNCTIONS AND HIRZEBRUCH–ZAGIER CYCLES
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 6 / November 2020
- Published online by Cambridge University Press:
- 20 February 2019, pp. 1947-1992
- Print publication:
- November 2020
-
- Article
- Export citation
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Let
$L/F$ be a quadratic extension of totally real number fields. For any prime 
$p$ unramified in 
$L$, we construct a 
$p$-adic 
$L$-function interpolating the central values of the twisted triple product 
$L$-functions attached to a 
$p$-nearly ordinary family of unitary cuspidal automorphic representations of 
$\text{Res}_{L\times F/F}(\text{GL}_{2})$. Furthermore, when 
$L/\mathbb{Q}$ is a real quadratic number field and 
$p$ is a split prime, we prove a 
$p$-adic Gross–Zagier formula relating the values of the 
$p$-adic 
$L$-function outside the range of interpolation to the syntomic Abel–Jacobi image of generalized Hirzebruch–Zagier cycles.
