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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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$U_p$ operator is not compact on $p$-adic modular forms

I know that one of the reasons for introducting overconvergent $p$-adic modular forms is that the $U_p$ operator is compact on them. Is there an easy way to see that $U_p$ is not compact on non-over …
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