Exponential functions in prime characteristic

Mattarei, Sandro (2006) Exponential functions in prime characteristic. Aequationes mathematicae, 71 (3). pp. 311-317. ISSN 0001-9054

Full content URL: http://dx.doi.org/10.1007/s00010-005-2816-4

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Abstract

In this note we determine all power series

F(X)∈1+XF p [[X]]
F(X)∈1+XFp[[X]]
such that (F(X + Y))−1F(X)F(Y) has only terms of total degree a multiple of p. Up to a scalar factor, they are all the series of the form F(X) = Ep(cX)· G(Xp) for some

c∈F p
c∈Fp
and

G(X)∈1+XF p [[X]]
G(X)∈1+XFp[[X]]
, where

E p (X)=exp(∑ i=0 ∞ X p i /p i )
Ep(X)=exp(∑i=0∞Xpi/pi)
is the Artin–Hasse exponential.

Keywords:Functional equation, Exponential series, Artin-Hasse exponential
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:18511
Deposited On:17 Feb 2017 08:47

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