In this paper we considered a moving from classical logic and Kolmogorov’s probability theory to non-classical p-adic valued logic and p-adic valued probability theory. Namely, we defined p-adic valued logic and further we constructed probability space for some ideals on truth values of p-adic valued logic. We proposed also p-adic valued inductive logic. Such a logic was considered for the firs...

In this largely expository paper we extend properties of the homological duality functor $RHom_{\mathcal H}(-,{\mathcal H})$ where ${\mathcal H}$ is Hecke algebra a reductive $p$-adic group, to case it finite central extension group. The most important being that concentrated in single degree for irreducible representations and gives rise Schneider--Stuhler Ext groups (a Serre like property). A...

In this article, we study p-adic torus periods for certain p-adic valued functions on Shimura curves coming from classical origin. We prove a p-adic Waldspurger formula for these periods, as a generalization of the recent work of Bertolini, Darmon, and Prasanna. In pursuing such a formula, we construct a new anti-cyclotomic p-adic L-function of Rankin– Selberg type. At a character of positive w...

We give a proof of the irrationality of the p-adic zeta-values ζp(k) for p = 2, 3 and k = 2, 3. Such results were recently obtained by F.Calegari as an application of overconvergent p-adic modular forms. In this paper we present an approach using classical continued fractions discovered by Stieltjes. In addition we show irrationality of some other p-adic L-series values, and values of the p-adi...

We consider distinction of representations in the context p $p$ -adic Galois symmetric spaces. provide new sufficient conditions for parabolically induced terms similar on inducing data and deduce a characterization from cuspidal. explicate results further classical groups give several applications, particular, concerning preservation via Langlands functoriality. relate our with conjecture Dipe...