TY - JOUR
T1 - On the universal power series for Jacobi sums and the vandiver conjecture
AU - Ichimura, Humio
AU - Kaneko, Masanobu
PY - 1989/3
Y1 - 1989/3
N2 - We shall study some explicit connections between (1) the Vandiver conjecture on the class number of the real cyclotomic field Q(cos(2π/l)) and (2) the images of various Galois representations induced from the power series representation (constructed and studied by Ihara, Anderson, Coleman, etc.) of Gal(Q/Q(μI∞)) which describes universally the Galois action on the Fermat curves of l-power degrees. One such connection was first discovered by Coleman. In the case of the original power series representation, we shall also describe the difference between the "expected image" and the actual Galois image in terms of a certain invariant of Iwasawa type.
AB - We shall study some explicit connections between (1) the Vandiver conjecture on the class number of the real cyclotomic field Q(cos(2π/l)) and (2) the images of various Galois representations induced from the power series representation (constructed and studied by Ihara, Anderson, Coleman, etc.) of Gal(Q/Q(μI∞)) which describes universally the Galois action on the Fermat curves of l-power degrees. One such connection was first discovered by Coleman. In the case of the original power series representation, we shall also describe the difference between the "expected image" and the actual Galois image in terms of a certain invariant of Iwasawa type.
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U2 - 10.1016/0022-314X(89)90076-0
DO - 10.1016/0022-314X(89)90076-0
M3 - Article
AN - SCOPUS:38249021317
VL - 31
SP - 312
EP - 334
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 3
ER -