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Let p be a prime $$\geq 5$$ and let $$\Lambda ={\mathcal O}[[X]]$$ where $${\mathcal O}$$ is the ring of p-adic integers of a finite extension of $${\mathbb{Q}}_ p$$. Let F and G be two ordinary $$\Lambda$$-adic modular forms. In his previous two papers [Invent. Math. 79, 159-195 (1985; Zbl 0573.10020); Ann. Inst. Fourier 38, No.3, 1-83 (1988; Zbl 0645.10028)] the author constructed a p-adic Rankin product $${\mathcal D}_ p$$ which p-adically interpolates (essentially) the critical special values $$D(m,f_ k,g_{\ell}| \omega^{-m})/(f_ k,f_ k)$$ where $$f_ k$$ resp. $$g_{\ell}$$ are specializations of F resp. G in weight k resp. $$\ell$$, $$\omega$$ is the Teichmüller character, D(s,f,g) is the usual Rankin L- series and (,) denotes the usual Petersson scalar product. As the author remarks, although the underlying ideas are simple the actual construction of $${\mathcal D}_ p$$ is rather involved due to the fact that one works in the general case of I-adic modular forms for every finite extension I of $$\Lambda$$.
In the present paper the author restricts to the special case of $$\Lambda$$-adic modular forms which have primitive “Nebentypus” and shows that in this case $${\mathcal D}_ p$$ can be constructed in a rather simple way.
 11F85 $$p$$-adic theory, local fields 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.) 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols