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- W3202711853 abstract "Let p be a prime $$ge 5$$ . We establish explicit rates of overconvergence for some members of the “Eisenstein family”, notably for the p-adic modular function $$V(E_{(1,0)}^{*})/E_{(1,0)}^{*}$$ (V the p-adic Frobenius operator) that plays a pivotal role in Coleman’s theory of p-adic families of modular forms. The proof goes via an in-depth analysis of rates of overconvergence of p-adic modular functions of form $$V(E_k)/E_k$$ where $$E_k$$ is the classical Eisenstein series of level 1 and weight k divisible by $$p-1$$ . Under certain conditions, we extend the latter result to a vast generalization of a theorem of Coleman–Wan regarding the rate of overconvergence of $$V(E_{p-1})/E_{p-1}$$ . We also comment on previous results in the literature. These include applications of our results for the primes 5 and 7." @default.
- W3202711853 created "2021-10-11" @default.
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- W3202711853 date "2021-10-06" @default.
- W3202711853 modified "2023-09-27" @default.
- W3202711853 title "Eisenstein series, p-adic modular functions, and overconvergence" @default.
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- W3202711853 doi "https://doi.org/10.1007/s40993-021-00292-8" @default.
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