P-adic Analysis Compared With Real

By S. Katok. 2007

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Rethinking Superdeterminism (2019, background): “But is this really so? In number theory there is an alternative to the class of Euclidean metrics (and indeed according to Ostrowsky’s theorem it is the only alternative): the p-adic metric [40].”
p-Adic Multiresolution Analysis and Wavelet Frames (2008, methodology): “Here and in what follows, we shall use the notation and the results from [32] (see also [8, 10]).”
Sub-Weyl subconvexity for Dirichlet $L$-functions to prime power moduli (2014, methodology): “ For example, the pair ( 1 2, 2), given by the p-adic exponent datum (36) ω 1/2 = 1 2, 1 2,0,1, κ+ι′ +1+ι′(12),max(κ −⌊λ⌋+ι′ +1,1),1+ ι′(4),ρp , is well suited for very long sums (4), yielding in (15) the upper bound X M<m6M+B e f(m) pn ≪ pn−w−κ−ι′ 1/2 logpn−w−κ−ι′, valid for all pnand f ∈ F(”