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Is there any application of Banach fixed point theorem in number theory? I have seen some applications in integral equations and economics. I am curious about number theory.

stephan
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  • Possibly in the p-adic numbers , but apart from that I guess not. – Peter Oct 13 '22 at 12:21
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    A small example here: the Banach fixed point theorem can be used to prove the existence of the Teichmuller character: https://math.stackexchange.com/a/3823717/232 – Qiaochu Yuan Oct 13 '22 at 16:38

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