Hida, Haruzo \(p\)-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 Cited in 1 ReviewCited in 4 Documents 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 Keywords:p-adic interpolation; spectrum of nearly ordinary Hecke algebra; two- variable p-adic L-function; symmetric square L-functions; cusp forms of integral weights; half-integral weight; p-adic modular forms; p-adic Hecke algebras; p-adic Rankin convolutions Citations:Zbl 0656.10022; Zbl 0684.00004; Zbl 0573.10020; Zbl 0645.10028; Zbl 0656.10023 PDF BibTeX XML OpenURL