Let F be a number field, and π an isobaric ([La]), algebraic ([Cl1]) automorphic representation of GLn(AF ). We will call π quasi-regular iff at every archimedean place v of F , the associated n-dimensional representation σv of the Weil group WFv (defined by the archimedean local correspondence) is multiplicity free. For example, when n = 2 and F = Q, a cuspidal π is quasi-regular exactly when ...

Stochastic processes on manifolds over non-Archimedean fields and with transition measures having values in the field C of complex numbers are studied. Stochastic antideriva-tional equations (with the non-Archimedean time parameter) on manifolds are investigated. 1. Introduction. Stochastic processes and stochastic differential equations on real Banach spaces and manifolds on them were intensiv...

This paper generalizes Yu. Manin’s approach toward a geometrical interpretation of Arakelov theory at infinity to linear cycles in projective spaces. We show how to interpret certain non-Archimedean Arakelov intersection numbers of linear cycles on Pn−1 with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n). This geometric setting has an Archimedean analogue, namely, t...

We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into n-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and p-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists...

‖b+ c‖ ≤ max (‖b‖, ‖c‖) then the value ‖b‖ is called non-archimedean. The thus delimited nonarchimedean values are of considerable arithmetic interest. They are useful in questions of divisibility and irreducibility and in fact often correspond exactly to the prime ideals of the given ring. This paper is devoted to the explicit construction of non-archimedean values. More specifically, given al...

The subject matter of p-adic uniformization of Shimura varieties starts with Cherednik’s paper [6] in 1976, although a more thorough historical account would certainly involve at least the names of Mumford and Tate. Cherednik’s theorem states that the Shimura curve associated to a quaternion algebra B over a totally real field F which is split at precisely one archimedean place v of F (and rami...

In this paper I show that a kind of infinite-order predicate logic can be regarded as non-Archimedean or p-adic valued. I have considered two principal versions of non-Archimedean valued predicate logical calculi: p-adic valued extension of BL∀ and hyper-valued extension of à LΠ∀. These logical systems are considered for the first time. c ©2010 World Academic Press, UK. All rights reserved.

1.1. Motivation. This paper is largely concerned with constructing quotients by étale equivalence relations. We are inspired by questions in classical rigid geometry, but to give satisfactory answers in that category we have to first solve quotient problems within the framework of Berkovich’s k-analytic spaces. One source of motivation is the relationship between algebraic spaces and analytic s...

Let 5 be a commutative semigroup. For a, b £5, we say that a divides b (or b is a multiple of a), and write a\b, if either a = b or ax = b for some x£5. We say that a properly divides b if a\b and b does not divide a. We call 5 archimedean if for all a, b £5, a divides some power of b. It is known that every commutative semigroup is uniquely expressible as a semilattice of archimedean semigroup...