LOCALLY COMPACT FIELDS Contents 5. Locally compact fields 1
... Note that L(t) and E(t) are precisely the usual Taylor series expansions of log(t) at t = 1 and et at = 0 encountered in real/complex analysis. a) Consider L(x) and E(x) as functions on, say, Cp . Show that the radius of con−1 vergence of L(x) is 1 and the radius of convergence of E(x) is Rp := p p− ...
... Note that L(t) and E(t) are precisely the usual Taylor series expansions of log(t) at t = 1 and et at = 0 encountered in real/complex analysis. a) Consider L(x) and E(x) as functions on, say, Cp . Show that the radius of con−1 vergence of L(x) is 1 and the radius of convergence of E(x) is Rp := p p− ...
Linear recursions over all fields
... where the hat indicates an omitted factor in the ith term, for every i. Each term in this sum is a polynomial, and all the terms besides the one for i = r have (1−λr x)er as a factor. Thus the term at i = r is divisible by (1−λr x)er . That term is qr (x)(1−λ1 x)e1 · · · (1−λr−1 x)er−1 . Since λ1 , ...
... where the hat indicates an omitted factor in the ith term, for every i. Each term in this sum is a polynomial, and all the terms besides the one for i = r have (1−λr x)er as a factor. Thus the term at i = r is divisible by (1−λr x)er . That term is qr (x)(1−λ1 x)e1 · · · (1−λr−1 x)er−1 . Since λ1 , ...
Lecture notes on Witt vectors
... Proof. One easily verifies that both sides of each equation have the same image by the ghost map. This shows that the relations hold, if A is torsion free, and hence, in general. ...
... Proof. One easily verifies that both sides of each equation have the same image by the ghost map. This shows that the relations hold, if A is torsion free, and hence, in general. ...
