Combinatorial Congruences and $ψ$-Operators

Daqing Wan

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Combinatorial Congruences and $ψ$-Operators

Daqing Wan

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Abstract

The $ψ$-operator for $(ϕ, Γ)$-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 (1977).

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Daqing Wan. 2005-08-16. Combinatorial Congruences and $ψ$-Operators. https://arxiv.org/abs/math/0508159

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