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.
"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