An action for a prospect of $p$-adic open superstring on target Minkowski space is proposed. The constructed `worldsheet' fields taking values in the field $\mathbb{Q}_p$, but it assumed to be obtained from discrete Bruhat-Tits tree. This proven have an analog worldsheet supersymmetry and superspace also terms superfields. does not conformal symmetry, however implemented definition amplitudes. ...

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential for...

We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the naive height into an archimedean and a non-archimedean term. Our main contribution is an algorithm for the computation of the non-archimedean term that require...

Non-archimedean seminorms on rings and modules provide in general a structure which is richer than the associated linear topology [3], [2]. We want to characterize Banach spaces and commutative algebras over a complete non-trivially valued nonarchimedean field K, as linearly topologized modules over the ring of integers K◦ of K, with no reference to any specific norm. This is analog to the clas...

A complex manifold X is said to be hyperbolic (in the sense of Brody) if every analytic map from the complex plane C to X is constant. From Picard’s “little” theorem, an entire function missing more than two values must be constant. It is equivalent to say that P \ {0, 1,∞} is hyperbolic. Picard’s theorem also show that a Riemann surface of genus one omitting one point and Riemann surfaces of g...

Quasi-invariant measures with values in non-Archimedean fields on a group of diffeomorphisms were constructed for non-Archimedean manifolds M in [Lud96, Lud99t]. On non-Archimedean loop groups and semigroups they were provided in [Lud98s, Lud00a, Lud02b]. A Banach space over a local field also serves as the additive group and quasi-invariant measures on it were studied in [Lud03s2, Lud96c]. Thi...

In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.

In the present paper, a partial order on a non- Archimedean fuzzymetric space under the  Lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.