214 research outputs found
p-adic number theory and its applications in a cryptographic form
Imperial Users onl
On a theory of the -function in positive characteristic
We present a theory of the -function (or Bernstein-Sato polynomial) in
positive characteristic. Let be a non-constant polynomial with coefficients
in a perfect field of characteristic Its -function is
defined to be an ideal of the algebra of continuous -valued functions on
The zero-locus of the -function is thus naturally
interpreted as a subset of which we call the set of roots of
We prove that has finitely many roots and that they are negative
rational numbers. Our construction builds on an earlier work of Musta\c{t}\u{a}
and is in terms of -modules, where is the ring of Grothendieck
differential operators. We use the Frobenius to obtain finiteness properties of
and relate it to the test ideals of Comment: Final versio
On the complexity of algebraic number I. Expansions in integer bases
Let be an integer. We prove that the -adic expansion of every
irrational algebraic number cannot have low complexity. Furthermore, we
establish that irrational morphic numbers are transcendental, for a wide class
of morphisms. In particular, irrational automatic numbers are transcendental.
Our main tool is a new, combinatorial transcendence criterion
On K(1)-local SU-bordism
This paper works towards a K(1)-local multiplicative splitting of SU-bordism
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