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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.
Frederic Arnold Kummer Sr. (August 5, 1873 – November 22, 1943) was an American author, playwright and screenwriter. He also used the pseudonym Arnold Fredericks . Several of his works were made into movies.
A Kummer extension is a field extension L/K, where for some given integer n > 1 we have K contains n distinct nth roots of unity (i.e., roots of X n − 1) L/K has abelian Galois group of exponent n. For example, when n = 2, the first condition is always true if K has characteristic ≠ 2.
In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst Kummer, who made a conjecture about the statistical properties of their arguments, as complex numbers. These sums were known and used before Kummer, in the theory of cyclotomy.
Austin Robert Butler (born August 17, 1991) is an American actor. Butler began his career on television, first in roles on Disney Channel and Nickelodeon, most notably on Zoey 101 (2007–2008), and later on teen dramas, including recurring parts on The CW's Life Unexpected (2010–2011) and Switched at Birth (2011–2012).
1 of 60 sheets Page 1 to 4 of 167 09/25/2012 12:19:02 AM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 IN THE COURT OF COMMON PLEAS OF ...
where φ(p a+1) is the Euler totient function, evaluated at p a+1 and a is a non negative integer. At a = 0, the expression takes the simpler form, as seen above. The two sides of the Kummer congruence are essentially values of the p-adic zeta function , and the Kummer congruences imply that the p -adic zeta function for negative integers is ...
Paul Kummer (22 August 1834 – 6 December 1912) was a minister, teacher, and scientist in Zerbst, Germany, known chiefly for his contribution to mycological nomenclature. Earlier classification of agarics by pioneering fungal taxonomist Elias Magnus Fries designated only a very small number of genera , with most species falling into Agaricus .