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Title: p-adic families of Yoshida lifts

Abstract: We construct a Hida family of Yoshida lifts for two given Hida families of modular forms, and compute the Petersson inner products of its specializations. The key step in the construction is to choose suitable Schwartz functions at p. The computation of the Petersson inner products can be viewed as a generalization of the computation in the works by Bocherer-Dummigan-Schulze-Pillot and Hsieh-Namikawa.