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2010 58 1 39 59 c 2010 20 2009 11 30 2010 6 24 6 25 1 1953 12 2008 III 1. 5, 1961, 1970, 1975, 1982, 1992 12 2008 2008 226 0015 32 40 58 1 2010 III 2., 2009 3 #3.xx #3.1 #3.2 1 1953 2 1958 12 2008 1 2

D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j

6 6.. [, b] [, d] ij P ij ξ ij, η ij f Sf,, {P ij } Sf,, {P ij } k m i j m fξ ij, η ij i i j j i j i m i j k i i j j m i i j j k i i j j kb d {P ij } lim Sf,, {P ij} kb d f, k [, b] [, d] f, d kb d 6..

a, b a bc c b a a b a a a a p > p p p 2, 3, 5, 7,, 3, 7, 9, 23, 29, 3, a > p a p [ ] a bp, b p p cq, c, q, < q < p a bp bcq q a <

22 9 8 5 22 9 29 0 2 2 5 2.............................. 5 2.2.................................. 6 2.3.............................. 8 3 8 4 9 4............................. 9 4.2 S(, a)..............................

20 6 4 1 4 1.1 1.................................... 4 1.1.1.................................... 4 1.1.2 1................................ 5 1.2................................... 7 1.2.1....................................

２０１２年１月号　０６１１５８／表２対向

(H8) 1,412 (H9) 40,007 (H15) 30,103 851

(H8) 1,412 (H9) 40,007 (H15) 30,103 851 (H3) 1,466 (H3) 9,862 (H15) 4,450 704 9,795 1,677 18,488 402 44,175 3,824 8,592 853 7,635 1,695 2,202 179 5,127 841 27,631 452 35,173 177 123,797 186 45,727 1,735

22 25 34 44 10 12 14 15 11 12 16 18 19 20 21 11 12 22 10 23 24 12 25 11 12 2611 27 11 28 10 12 29 10 30 10 31 32 10 11 12 33 10 11 12 34

22 25 34 44 10 12 14 15 11 12 16 18 19 20 21 11 12 22 10 23 24 12 25 11 12 2611 27 11 28 10 12 29 10 30 10 31 32 10 11 12 33 10 11 12 34 35 10 12 36 10 12 37 10 38 10 11 12 39 10 11 12 40 11 12 41 10 11

- 1 - - 2 - - 3 - - 4 - H19 H18-5 - H19.7H20.3 8,629 11,600-6 - - 7 - - 8 - - 9 - H20.7 20 / - 10 - - 11 - 1 8,000 16,000 4,000 2 50 12 80-12 - 20 3040 50 18a 19a - 13 - - 14 - 1,000-15 - 3,000 4,500 560

17 12 12 13301515 2F1 P2 1 22 P19 160

136 17 12 12 13301515 2F1 P2 1 22 P19 160 161 15 87 15 P5 26 4 162 10 3 60 1/3 3 1 163 137 138 139 % %.%. (. ) ( ) 48 32 13 40 43 30 42 50 13 99 140 39 12 12 42 55 35 6 79 2004 16 17 39 37 53 13 1 1.2

ﾀ 縺29135 ﾀ 縺5 [ y 1 x i R 8 x j 1 7,5 2 x , ﾁ7192, (2) ﾁ41299 f 675

139ｨ 48 1995 3. 753 165, 2 6 86 ﾀ7 9 998917619 4381 縺48 縺55 317832645 ﾀ5 縺4273 971927, 95652539358195 45 ﾁ5197 9 4527259495 2 7545953471 129175253471 9557991 3.9. ﾀ52917652 縺1874ｨ 989 95652539358195 45

X G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2

149 (Newell [5]) Newell [5], [1], [1], [11] Li,Ryu, and Song [2], [11] Li,Ryu, and Song [2], [1] 1) 2) ( ) ( ) 3) T : 2 a : 3 a 1 :

Transactions of the Operations Research Society of Japan Vol. 58, 215, pp. 148 165 c ( 215 1 2 ; 215 9 3 ) 1) 2) :,,,,, 1. [9] 3 12 Darroch,Newell, and Morris [1] Mcneil [3] Miller [4] Newell [5, 6], [1]

2 (2016 3Q N) c = o (11) Ax = b A x = c A n I n n n 2n (A I n ) (I n X) A A X A n A A A (1) (2) c 0 c (3) c A A i j n 1 ( 1) i+j A (i, j) A (i, j) ã i

[ ] (2016 3Q N) a 11 a 1n m n A A = a m1 a mn A a 1 A A = a n (1) A (a i a j, i j ) (2) A (a i ca i, c 0, i ) (3) A (a i a i + ca j, j i, i ) A 1 A 11 0 A 12 0 0 A 1k 0 1 A 22 0 0 A 2k 0 1 0 A 3k 1 A rk

1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =

1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i

newmain.dvi

数論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published

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