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Combinatorial congruences and ψ-operators

Abstract

The ψ-operator for (φ{symbol}, Γ)-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 ψ-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 [Some congruences for binomial coefficients, Michigan Math. J. 24 (1977) 141-151]. © 2005 Elsevier Inc. All rights reserved.

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