## $$p$$-adic $$L$$-functions for base change lifts of $$\mathrm{GL}_ 2$$ to $$\mathrm{GL}_ 3$$.(English)Zbl 0705.11033

Automorphic forms, Shimura varieties, and L-functions. Vol. II, Proc. Conf., Ann Arbor/MI (USA) 1988, Perspect. Math. 11, 95-142 (1990).
[For the entire collection see Zbl 0684.00004.]
The author constructs a two-variable $$p$$-adic $$L$$-function which $$p$$-adically interpolates critical values of the symmetric square $$L$$-functions attached to cusp forms of integral weights. The proof uses generalization to the case of half-integral weight of the author’s results on $$p$$-adic modular forms of integral weight and $$p$$-adic Hecke algebras and the method of $$p$$-adic Rankin convolutions as developed by the author [cf. Invent. Math. 79, 159–195 (1985; Zbl 0573.10020); Ann. Inst. Fourier 38, No. 3, 1–83 (1988; Zbl 0645.10028)]. To prove that the $$L$$-functions obtained are holomorphic an idea of C.-G. Schmidt [Invent. Math. 92, 597–631 (1988; Zbl 0656.10023)] is adopted.
Reviewer: W.Kohnen

### MSC:

 11F85 $$p$$-adic theory, local fields 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols 11S40 Zeta functions and $$L$$-functions