-4
votes
3answers
504 views

Books on analytic functions on Banach spaces over a non-Archimedean field

I'm looking for good textbooks on analytic functions on Banach spaces over a non-Archimedean field. If you know one(s), please let me know.
6
votes
1answer
390 views

A p-adic analogue for a formula of Riemann?

This might be naive question but I was wondering whether a p-adic analogue of the following (shockingly) beautiful formula $$\zeta(s)\Gamma(s) = \int_0^\infty \frac{t^{s-1}}{e^t-1} dt$$ (vaild for ...
13
votes
1answer
684 views

P-adic C* algebras

I understand that there is a definition of p-adic Banach algebras and that a significant amount of functional analysis can be developed in the non-archimedean setting. Is there a p-adic version of ...
16
votes
3answers
2k views

An unfamiliar (to me) form of Hensel's Lemma

In his very nice article Peter Roquette, History of valuation theory. I. (English summary) Valuation theory and its applications, Vol. I (Saskatoon, SK, 1999), 291--355, Fields Inst. Commun., ...