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The convergence of the series depends crucially on the p-adic norm of its terms.
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The convergence of the series depends crucially on the p-adic norm of its terms.
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Related words
p-adic norm
Noun
(number
theory)
A
p-adic
absolute
value,
for
a
given
prime
number
p,
the
function,
denoted
|..|ₚ
and
defined
on
the
rational
numbers,
such
that
|0|ₚ
=
0
and,
for
x≠0,
|x|ₚ
=
p^(-ordₚ(x)),
where
ordₚ(x)
is
the
p-adic
ordinal
of
x;
the
same
function,
extended
to
the
p-adic
numbers
ℚₚ
(the
completion
of
the
rational
numbers
with
respect
to
the
p-adic
ultrametric
defined
by
said
absolute
value);
the
same
function,
further
extended
to
some
extension
of
ℚₚ
(for
example,
its
algebraic
closure).
Japanese Meaning
（数論）素数pに対して定義されたp進絶対値。0の場合は0、非0の場合は|x|ₚ = p^(－ordₚ(x))となる。 / 有理数上に定義され、さらにp進数体ℚₚやその拡大体上へ拡張される関数。
Related Words
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