: ��ʸ��ˤĤ��...

��I�� No.10

��Υơ��

$\fbox{��Ϥι�Ʊ��ؿ�}$

�ʲ� ��ǿ��Ǥ��Ȥ�� ( ��)�Ǥ��Ȥ��롣

�Ĥ��ѿ� $X_1,\dots,X_n$ �˴ؤ�� $% latex2html id marker 783 $ {\mathbb{F}}_q$$ �� ¿�༰ $f_1,f_2,\dots,f_m$ ��Ϳ��Ƥ��Ȥ��

	$\displaystyle f_1(X_1,X_2,\dots,X_n)=0,$
	$\displaystyle f_2(X_1,X_2,\dots,X_n)=0,$
	$\displaystyle f_3(X_1,X_2,\dots,X_n)=0,$
	$\displaystyle \dots ,$
	$\displaystyle \dots ,$
	$\displaystyle f_m(X_1,X_2,\dots,X_n)=0$

�� $V(f_1,\dots,f_m)$ ��뤤�� ( $f_1,f_2,\dots,f_m$ ��狼�꤭�äƤ��ˤ�)

�Ǥ��魯�� $% latex2html id marker 799 $ {\mathbb{F}}_{q^r}$$ �Ǥ� $V(f_1,\dots,f_m)$ �β��Τ� $% latex2html id marker 803 $ V(f_1,\dots,f_m)({\mathbb{F}}_{q^r})$$ �ǽ�ɽ��

�� 10.1 ��

�ι�Ʊ��ؿ��

$% latex2html id marker 808 $ \displaystyle Z(V,t)= \exp \left ( \sum_{k=1}^\infty \frac{\char93 V({\mathbb{F}}_{q^k})}{k}t^k \right) $$

�ˤ�ä��롣�� $% latex2html id marker 810 $ {\mathbb{F}}_q$$ ��ϡ� $% latex2html id marker 812 $ Z(V/{\mathbb{F}}_q,t)$$ �ʤɤȤ�񤯡�

�ºݤϱ��դε��ϼ�«��Τ�� Ǥϼ�«��ϵ��ˤ��ˡַ��Ū�٤��פȤ��ư��Ȥˤ��롣

$\displaystyle \sum_{k=1}^\infty \frac{t^k}{k}=- \log(1-t)$

�ˤ��դ��Ƥ��

�� 10.1 2�Ĥ��ѿ�

�˴ؤ��

��Ф��ơ�

.

�� 10.2 2�Ĥ��ѿ�

�˴ؤ��

��Ф��ơ�

�� 10.3 2�Ĥ��ѿ�

�˴ؤ��

��Ф��ơ�

�ѿ��ĤΤȤ��ϡ��̿��ˤ�äƹ�Ʊ��ؿ��ޤ롣

̿�� 10.1

�� $% latex2html id marker 840 $ {\mathbb{F}}_q$$ ��ʰ��ѿ�

��¿�༰�Ǥ��Ȥ��롣 1�Ĥ��ѿ�

�˴ؤ��

�ˤĤ��ơ�

$\displaystyle Z(V,t)=\frac{1}{1-t^d}$

��Ω�ġ�

��Ǥʤ��Ȥ��Ϥɤ��򻲾ȤΤ��ȡ�

�� 10.1

�ϴ��ǿ��ζҤǤ��Ȥ��롣��ΤȤ� 1�Ĥ��ѿ�

�˴ؤ��

��Ф��ơ� $% latex2html id marker 859 $ Z(V/{\mathbb{F}}_q,t)$$ ��ʤ��

�� 10.2 1�Ĥ��ѿ�

�˴ؤ��

��Ф��ơ� $Z(V/{\mathbb{F}}_5,t)$ ��ʤ��

ʿ��16ǯ12��9��