 About 3,290 results  books.google.com Barry Mazur, Glenn Stevens  1994  Preview PROOF: Let V be the associated representation space of pm and Set d = dimk V
and consider W = V® (Hom(V",Mp) ® xfc~V) , where x is the pcyclotomic
character and e((.) = (() e k = T/m is the Neben typus character. By the Eichler
Shimura ... 

 books.google.com ... of the complex Lfunction associated to 6 with Euler factors at primes in EU
removed. The padic cyclotomic character of F is denoted by K i.e. it is a
homomorphism K: Gal(F/F)—> Z; defined by g f I $45'), for all g G Gal(F/F) and
allE G ,apoo. 

 books.google.com The cyclotomic theory. This section will be devoted to a brief account of the padic
analogue of the Riemann zeta function. Recalling that X is given by (4), we write
Xalg for the subgroup of X consisting of all characters of the form E,=\!1\x (ne Z) ... 

 books.google.com of Nth roots of unity for any ring A. Let Q be the totality of algebraic numbers in C.
We consider the cyclotomic field Q(uN). ... We simply write X, for Xp. By taking the
projective limit, we get the padic cyclotomic character x = imax, : Gal(Q.5/Q) ... 

 books.google.com We view without comment a character of Gal(Qp /F) as a character of F×. We
denote by ε the padic cyclotomic character. It corresponds to the character of F×
given by x→ xF ∏ σ∈S σ(x). A padic norm on an Evector space V is a function
... 

 books.google.com For each place p of Q, we fix embeddings ιp of Q in its completions Qp. Denote by
χp the padic cyclotomic character, and ωp the Teichm ̈uller lift of the mod p
cyclotomic character χp (the latter being the reduction mod p of χp). By abuse of ... 

 books.google.com We fix a prime p > 2 and write   p for the p—adic absolute value on Q nor1
malized so that pp I 5. ... p/Qp) is upper triangular with diagonal characters Naj
on the inertia I}, for the padic cyclotomic character N ordered from top to bottom
as a1 ... 

 books.google.com Let p be a prime number, and let K be a finite extension of Qp. Let N > 1 be an
integer relatively prime to p, f € S1(N)K a ... unramified characters of GQ, whose
value at pp are a and 3, respectively. Let X be the padic cyclotomic character.
Then ... 

 books.google.com The other 0 Â is the constant term modulo Â of a adic modular form that appears
in a computation of the regulators of zeta elements. 2.7.2. The map HS ... The
map ÄWGQ ! Zp is the padic cyclotomic character, and log is the padic logarithm
. 

 books.google.com GROUP. CHARACTERS. Let E be an elliptic curve over Q with complex
multiplication by the ring of integers OK. of an imaginary ... It is analogous to the
fact that the restriction to Gp — Gal(<Q^/Qp) of the padic cyclotomic character xP
: Go ~t ... 

 