Let p be a prime $$\ge 5$$ . We establish explicit rates of overconvergence for some members the “Eisenstein family”, notably p-adic modular function $$V(E_{(1,0)}^{*})/E_{(1,0)}^{*}$$ (V Frobenius operator) that plays pivotal role in Coleman’s theory families forms. The proof goes via an in-depth analysis functions form $$V(E_k)/E_k$$ where $$E_k$$ is classical Eisenstein series level 1 and we...

In the present paper, we prove that first homology group of Bianchi 3-fold is generated by special modular symbols. Also, construct integral valued p-adic L-function p-ordinary Hecke eigenforms taking Lefschetz-Poincaré Pairing cohomology class attached to forms and symbols on 3-folds. By using generation result, μ-invariant some isotopic components certain vanishes for a positive proportion or...