منابع مشابه
THE METRIC THEORY OF p−ADIC APPROXIMATION
Abstract. Metric Diophantine approximation in its classical form is the study of how well almost all real numbers can be approximated by rationals. There is a long history of results which give partial answers to this problem, but there are still questions which remain unknown. The Duffin-Schaeffer Conjecture is an attempt to answer all of these questions in full, and it has withstood more than...
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We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work of Colmez on p-adic Green functions. We introduce the p-adic version of a metrized line bundle and define the met...
متن کاملP-adic Nori Theory
Given a fixed integer n, we consider closed subgroups G of GLn(Zp), where p is sufficiently large in terms of n. Assuming that the Zariski closure of G in GLn has no toric part, we give a condition on the (mod p) reduction of G which guarantees that G is of bounded index in GLn(Zp) ∩ G(Qp). In [No], Nori considered a special class of subgroups of GLn(Fp), namely groups which are generated by el...
متن کاملp-Adic Fourier Theory
In this paper we generalize work of Amice and Lazard from the early sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the open unit disk over Cp. Lazard showed that this ring has a divisor theory and that the classes of closed, finitely generated, and principal ideals in this ring coincide. W...
متن کاملApproximation Lattices of p - adic Numbers
Approximation lattices occur in a natural way in the study of rational approximations to p-adic numbers. Periodicity of a sequence of approximation lattices is shown to occur for rational and quadratic p-adic numbers. and for those only, thus establishing a p-adic analogue of Lagrange’s theorem on periodic continued fractions. Using approximation lattices we derive upper and lower bounds for th...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2009
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnp114