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The Kummer extensions in this case also include biquadratic extensions and more general multiquadratic extensions. When K has characteristic 2, there are no such Kummer extensions. Taking n = 3, there are no degree 3 Kummer extensions of the rational number field Q, since for three cube roots of 1 complex numbers are required.
In mathematics, specifically in the field of numerical analysis, Kummer's transformation of series is a method used to accelerate the convergence of an infinite series.
Kummer made a statistical conjecture about θ p and its distribution modulo 2π (in other words, on the argument of the Kummer sum on the unit circle). For that to make sense, one has to choose between the two possible χ: there is a distinguished choice, in fact, based on the cubic residue symbol .
Kaspar Johann Kummer [1] (1795–1870) was a German flautist, professor and composer. Kummer was born on 10 December 1795 in Erlau in Thuringia (in Sankt Kilian .) [ 2 ] He taught himself the flute while learning violin, horn, trumpet, clarinet, bassoon, oboe, cello and double bassoon.