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December 2019 On Generalised Kummer Congruences and Higher Rank Iwasawa Theory at Arbitrary Weights
Kwok-Wing TSOI
Tokyo J. Math. 42(2): 585-610 (December 2019). DOI: 10.3836/tjm/1502179304

Abstract

In recent work Burns, Kurihara and Sano introduced a natural notion of (generalised) Stark elements of arbitrary rank and weight and conjectured a precise congruence relation between Stark elements of a fixed rank and different weights. This conjecture was shown to simultaneously generalise both the classical congruences of Kummer and the explicit reciprocity law of Artin-Hasse and Iwasawa. In this article, we show that the congruence conjecture also implies that the Iwasawa theoretical `zeta element’ that is conjecturally associated to the multiplicative group has good interpolation properties at arbitrary even integers.

Citation

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Kwok-Wing TSOI. "On Generalised Kummer Congruences and Higher Rank Iwasawa Theory at Arbitrary Weights." Tokyo J. Math. 42 (2) 585 - 610, December 2019. https://doi.org/10.3836/tjm/1502179304

Information

Published: December 2019
First available in Project Euclid: 24 August 2019

zbMATH: 07209635
MathSciNet: MR4106594
Digital Object Identifier: 10.3836/tjm/1502179304

Subjects:
Primary: 11S40

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
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Vol.42 • No. 2 • December 2019
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