OpenXM/doc/Papers/bfct.tex - diff

Return to bfct.tex CVS log

Up to [local] / OpenXM / doc / Papers

version 1.1, 2001/02/06 07:54:18

version 1.2, 2001/02/06 08:38:31

Line 1

% $OpenXM$

% $OpenXM: OpenXM/doc/Papers/bfct.tex,v 1.1 2001/02/06 07:54:18 noro Exp $

\documentclass{jarticle}

\usepackage[theorem,useeps,FVerb]{jssac}

\title{Risa/Asir $B$K$*$1$k(B Weyl Algebra $B>e$N%0%l%V%J4pDl7W;;$*$h$S$=$N1~MQ(B}

Line 135 $$

\begin{Th}

$$I=Id(t-y_1f,\partial_1+y_1 (\partial f/\partial x_1) \partial_t, \cdots,

\partial_n+ y_1 (\partial f/\partial x_n) f_n \partial_t)$$

\partial_n+ y_1 (\partial f/\partial x_n) \partial_t)$$

$B$KBP$7(B, $G_1$ $B$r(B $I_1 = I \cap D$ $B$N%0%l%V%J4pDl$H$9$k(B. $B$3$N;~(B,

$$Id(\psi(G_1)) \cap K[s] = Id(b(-s-1))$$

\end{Th}

Line 151 b-function $B$N$_$r5a$a$k>l9g$K$O(B, $BD>@\(B $K[s

\subsection{\Q $B>e$N(B Weyl Algebra $B$K$*$1$k:G>.B?9`<0$N(B modular $B7W;;(B}

\label{mod1}

$D$ $B$r(B $\Q$ $B>e$N(B Weyl Algebra, $J \subset D$, $P \in D$ $B$+$D(B $P$ $B$O@0(B

$D$ $B$r(B $\Q$ $B>e$N(B Weyl Algebra, $J$ $B$r(B $D$ $B$N(B ideal, $P \in D$ $B$+$D(B $P$ $B$O@0(B

$B?t78?t$H$7(B, $J\cap \Q[P] \neq \{0\}$ $B$H$9$k(B. $B$3$N;~(B, $J\cap \Q[P] =

Id(b(P))$ $B$H$9$l$P(B

$b(s)$ $B$O(B$D/J$ $B$K$*$1$k(B $P$ $B$N(B \Q $B>e$N:G>.B?9`<0$H$J$k(B.

$B$3$3$G(B, $b(s) \in \Z[s]$ $B$+$D(B \Z $B>e86;OE*$H<h$l$k(B.

$J$ $B$N(B, $B=g=x(B $<$ $B$K4X$9$k%0%l%V%J4pDl$G(B, $B3F85$NF,78?t$,(B 1 $B$G$"$k$b$N$r(B $G$

$B$H$7(B, $G$ $B$N3F85$N(B $B$N78?t$,(B $\Z_{(p)} = \{a/b | a\in \Z, b \notin

$B$H$7(B, $G$ $B$N3F85$N78?t$,(B $\Z_{(p)} = \{a/b | a\in \Z, b \notin

p\Z\}$ $B$KB0$9$k$h$&$J(B $p$$B$rA*$V(B. $\phi_p$ $B$r(B $\Z_{(p)}$ $B$+$i(B $GF(p)$

$B$X$NI8=`E*<M1F(B ($B$*$h$S$=$N(B $D$ $B$X$N3HD%(B) $B$H$9$k(B.

Line 245 $Id(\psi(G_1))\cap K[s]$$B$r(B Section \ref{mod1} $

$B$H$7$F5a$a$kJ}K!(B ($BJ}K!(B 2), $B$*$h$S(B Section \ref{mod2} $B$G=R$Y$?J}K!(B ($BJ}(B

$BK!(B 3)$B$K$h$k7W;;;~4V$r$5$^$6$^$JB?9`<0$KBP$7$FHf3S$9$k(B. $B$$$:$l$b(B,

$b$-function $B$N7W;;$O(Bmodular $B7W;;$G:G>.B?9`<05a$a$kJ}K!$K$h$j9T$C(B

$B$?(B. $BNcBj$O(B\cite{oaku-bfct}, \cite{yano-bfct} $B$+$i:N$C$?(B. $B8eH>$N(B

$B$?(B. $BNcBj$O(B\cite{oaku-bfct}, \cite{yano-bfct} $B$+$i:N$C$?(B. $BI=(B 2 $B$N(B

$x^a+xy^{b-1}+y^b$ $B$K4X$7$F$O(B, $BK\9V5fO?Cf$NBg0$5W(B, $B9b;3N>;a$K$h$k9F$r(B

$B;2>H(B. $B7W;;$O(B, PentiumIII 1GHz $B>e$G9T$C$?(B. $BC10L$OIC$G%,!<%Y%C%8%3%l%/%7%g(B

$B%s;~4V$O=|$$$F$"$k(B. ``--'' $B$O(B, $BB>$NJ}K!$HHf3S$7$F;~4V$,$+$+$j2a$.$k$?(B