In this article, we introduce a systematic new method to investigate the conjectural p-adic meromorphic continuation of Professor Bernard Dwork’s unit root zeta function attached to an ordinary family of algebraic varieties defined over a finite field of characteristic p. After his pioneer p-adic investigation of the Weil conjectures on the zeta function of an algebraic variety over a finite fi...

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...

We initiate and examine integer powers of the (possibly unbounded) diagonal operators on the so-called p-adic Hilbert space Eω (see [10], [11], and [3]). For that, we first give and recall the required background on author’s recent work related to the formalism of unbounded linear operators in the p-adic setting [5]. Next, we shall be dealing with integer powers of the diagonal operators, their...

Let $G$ be a split reductive group over the ring of integers in $p$ -adic field with residue $\mathbf {F}$ . Fix representation $\overline {\rho }$ absolute Galois an unramified extension {Q}_p$ , valued $G(\mathbf {F})$ We study crystalline deformation for fixed Hodge type that satisfies analog Fontaine–Laffaille condition -valued representations. In particular, we give root theoretic on which...