Uniqueness and quasimeasures on the group of integers of a 𝑝-series field

Wade, William R.; Yoneda, Kaoru

doi:10.1090/S0002-9939-1982-0637169-9

Uniqueness and quasimeasures on the group of integers of a $p$-series field
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by William R. Wade and Kaoru Yoneda

Proc. Amer. Math. Soc. 84 (1982), 202-206

DOI: https://doi.org/10.1090/S0002-9939-1982-0637169-9

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Erratum: Proc. Amer. Math. Soc. 88 (1983), 378.

Abstract:

Let $G$ be the group of integers of a $p$-series field and suppose that $S$ is a character series on $G$. If ${N_1}$, ${N_2}, \ldots$ is any sequence of integers and if ${S_{{p^{{N_j}}}}} \to 0$ a.e. on $G$, as $j \to \infty$, then $S$ will be the zero series provided $S$ never diverges unboundedly.

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