Source Word
p-adic absolute value
Noun
(number
theory,
field
theory)
A
norm
for
the
rational
numbers,
with
some
prime
number
p
as
parameter,
such
that
any
rational
number
of
the
form
pᵏ(a/b)
—
where
a,
b
and
k
are
integers
and
a,
b
and
p
are
coprime
—
is
mapped
to
the
rational
number
p⁻ᵏ
and
0
is
mapped
to
0.
(Note:
any
nonzero
rational
number
can
be
reduced
to
such
a
form.)
Japanese Meaning
（数論、体論）ある素数 p をパラメータとして、有理数全体に定義されるノルム（絶対値関数）で、任意の非零有理数が p の冪乗因子に基づいた一意の形、すなわち pᵏ (a/b)（ここで a, b, k は整数で、a, b および p が互いに素である形）に表現でき、その値を p⁻ᵏ と定義し、0 は 0 と対応させるというものです。
Sense（1）
(number
theory,
field
theory)
A
norm
for
the
rational
numbers,
with
some
prime
number
p
as
parameter,
such
that
any
rational
number
of
the
form
pᵏ(a/b)
—
where
a,
b
and
k
are
integers
and
a,
b
and
p
are
coprime
—
is
mapped
to
the
rational
number
p⁻ᵏ
and
0
is
mapped
to
0.
(Note:
any
nonzero
rational
number
can
be
reduced
to
such
a
form.)
（ plural ）
