In recent years, p-adic numbers are widely used in theoretical and mathematical physics cf. 1–8 , such as string theory, statistical mechanics, turbulence theory, quantum mechanics, and so forth. For a prime number p, let Qp be the field of p-adic numbers. It is defined as the completion of the field of rational numbers Q with respect to the non-Archimedean p-adic norm | · |p. This norm is defi...

In this paper, we prove that birational smooth minimal models over C have equal Hodge numbers in all dimensions by an arithmetic method. Our method is a refinement of the method of Batyrev on Betti numbers who used p-adic integration and the Weil conjecture. Our ingredient is to use further arithmetic results such as the Chebotarev density theorem and p-adic Hodge theory.

Abstract Scattering amplitudes in perturbative quantum field theory exhibit a rich structure of zeros, poles and branch cuts which are best understood complexified momentum space. It has been recently shown that by leveraging this information one can significantly simplify both analytical reconstruction final expressions for the rational coefficients transcendental functions appearing phenomeno...

Let p be a prime number. Let w2 and w ∗ 2 denote the exponents of approximation defined by Mahler and Koksma, respectively, in their classifications of p-adic numbers. It is well-known that every p-adic number ξ satisfies w∗ 2(ξ) ≤ w2(ξ) ≤ w∗ 2(ξ) + 1, with w∗ 2(ξ) = w2(ξ) = 2 for almost all ξ. By means of Schneider’s continued fractions, we give explicit examples of p-adic numbers ξ for which ...

Throughout this paper Zp, Qp, C and Cp will respectively denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. The p-adic absolute value in Cp is normalized so that |p|p = 1 p . When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C or a p-adic numbe...

In this paper, we investigate some properties for the (h, q)-tangent numbers and polynomials. By using these properties, we obtain some interesting identities on the (h, q)-tangent polynomials and Bernstein polynomials. Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion o...

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...