$B9)A!Bg$NDMK\$H?=$7$^$9(B.

In article <9f9e6a70-8e51-48a1-8982-d42d4d588643@k9g2000yqi.googlegroups.com>
KyokoYoshida <kyokoyoshida123@gmail.com> writes:
> $B&F(B(s)=$B&0(B_{p:prime number}1/(1-1/p^s)$B$r<($7$F$$$^$9!#(B
> 
> (1/2^s)$B&F(B(s)=1/2^s+1/4^s+1/6^s+$B!D(B
> (1-1/2^s)$B&F(B(s)=(1+1/3^s+1/5^s+1/7^s+$B!D(B)-(1/22^s+1/24^s+1/26^s+1/28^s+$B!D(B)

$B4V0c$C$F$$$^$9(B.

> (1-1/2^s)(1-1/3^s)$B&F(B(s)=(1+1/5^s+1/7^s+1/11^s+1/13^s+$B!D(B)-(1/22^s+1/24^s
> +1/26^s+1/28^s+1/30^s+\xE2
$B$d$O$j4V0c$C$F$$$^$9(B.

> (1-1/2^s)(1-1/3^s)(1-1/4^s)$BN6(B(s)=(1+1/5^s+1/7^s+1/11^s+1/13^s+1/17^s
> +1/19^s+$Bb>(B                                                        ⑧$B1/4^s+1/20^s(B
\xBE ɜ$(D??$B2^s+1/24^s(Bɜ$(D??$B6^s+1/30^s(B\xE2
$B$@$+$i(B, $B^A\xAE
> $B%Z!<%8$N<0(B(56)$B$+$i<0(B(61)$B$,;29M$K$7$?$N$G$9$,(B

$B5.J}$N<0$O;29M$K$7B;$M$F$$$^$9$M(B.
 
> 58$B9TL\$H(B59$B9TL\$H(B60$B9TL\$N1&JU(B
> (1+1/3^s+1/5^s+1/7^s+$B!D(B)-(1/3^s+1/9^s+1/15^s+$B!D(B)

$B$3$l$r7W;;$9$k$H(B, \sum_{n=1}^\infty 1/n^s $B$G(B
 n $B$,(B 2 $B$NG\?t$G$"$k$H$-$N9`(B 1/n^s $B$r=|$$$?$b$N$NFb$+$i(B,
$B99$K(B n $B$,(B 3 $B$NG\?t$G$"$k$H$-$N9`(B 1/n^s $B$r=|$/$3$H$K$J$j$^$9(B.

# $B!V=|$$$?$b$N$N(B *$BFb$+$i(B*, $B=|$/!W$H$$$&$H$3$m$,4N?4(B.

> $B$+$i(B
> $B&F(B(s)$B&0(B_{n=1}^$B!g(B(1-p_n^-s)

 \zeta(s) \prod_{n=1}^r (1 - (p_n)^{-s})

$B$r7W;;$9$k$H(B, \sum_{n=1}^\infty 1/n^s $B$+$i(B,
 n $B$,(B p_1, p_2, \dots, p_r $B$N$I$l$+$r0x?t$H$7$F(B
$B4^$`$H$-$N9`(B 1/n^s $B$r=|$$$?$b$N$NOB$K$J$j$^$9(B.

> $B$+$i(B
> 1
> $B$H$J$k$N$,$I$&$7$F$b$o$+$j$^$;$s!#(B

$B:G8e$K;D$k$N$O(B, $B$I$s$JAG?t(B p $B$b0x?t$H$7$F4^$^$J$$?t(B
 n = 1 $B$KBP1~$9$k9`(B 1/n^s = 1 $B$@$1$G$9(B.
-- 
$BDMK\@i=)(B@$B?tM}!&<+A3ItLg(B.$B4pHW2J3X7O(B.$B5~ET9)7]A!0]Bg3X(B
Tsukamoto, C. : chiaki@kit.ac.jp