Combinatorial Congruences and $ψ$-Operators

Details Combinatorial Congruences and $ψ$-Operators Combinatorial Congruences and $ψ$-Operators

2005-08-09

arxiv.org/abs/math/0508159v2

Mathematics

Number Theory

11 pages

Scientific paper

The $\psi$-operator for $(\phi, \Gamma)$-modules plays an important role in the study of Iwasawa theory via Fontaine's big rings. In this note, we prove several sharp estimates for the $\psi$-operator in the cyclotomic case. These estimates immediately imply a number of sharp $p$-adic combinatorial congruences, one of which extends the classical congruences of Fleck (1913) and Weisman (1977).

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