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On pi-adic expansion of singular integers of the p-cyclotomic field
Roland Queme
Let p be an odd prime. Let F_p^* be the no-null part of the finite field of p elements. Let K = Q(zeta) be the p-cyclotomic field and let O_K be the ring of integers of K. Let pi b…
On prime factors of class number of cyclotomic fields
Roland Queme
Let p be an odd prime. Let K = \Q(zeta) be the p-cyclotomic number field. Let v be a primitive root mod p and sigma : zeta --> zeta^v be a \Q-isomorphism of the extension K/\Q gene…
Singular Integers and Kummer-Stickelberger relation
Roland Queme
Let p be an odd prime. Let F_p^* be the no-null part of the finite field of p elements. Let K=\Q(zeta) be a p-cyclotomic field and O_K be its ring of integers. Let pi be the prime…
Singular integers and p-class group of cyclotomic fields
Roland Queme
Let be an irregular prime. Let $K=\Q(ζ)$ be the -cyclotomic field. From Kummer and class field theory, there exist Galois extensions $S/\Q$ of degree such that $S/K…
Singular numbers and Stickelberger relation
Roland Queme
Let p be an odd prime. Let K_p = Q(zeta) be the p-cyclotomic field. Let pi be the prime ideal of K_p lying over p. Let G be the Galois group of K_p. Let v be a primitive root mod p…
Some applications of Kummer and Stickelberger relations
Roland Queme
Let p be an odd prime. Let K = Q(zeta) be the p-cyclotomic field. Let v be any primitive root mod p. Let sigma be a Q-isomorphism of K. Let P(sigma) = sigma^{p-2}v^{-(p-2)}+ ... +…