- (E-mail: atsushi@math.tohoku.ac.jp) [ ] , , 21 9, , 2000.
- RATIONAL POINTS ON QUADRATIC TWISTS OF AN ELLIPTIC CURVE
- MM}EyJ,E@$r$b$DBJ1_6J@~$+$iF@$i$l$k BN$N3HBg$K$*$1$kJ,4t$K$D$$$F
- ON THE CLASS NUMBERS OF CERTAIN NUMBER FIELDS OBTAINED FROM POINTS ON ELLIPTIC CURVES II
- (n, n) n . A, B n , A + B AB n . tA n (
- " " , 1 " " . [1] E. ( ), , , 1974.
- ON THE CLASS NUMBERS OF CERTAIN NUMBER FIELDS OBTAINED FROM POINTS ON ELLIPTIC CURVES II #
- [1] , , 8, , 1990. [2] , , , 1976.
- Counting Rational Points on Projective Space with Certain Congruent Conditions
- Construction of Number Fields of Odd Degree with Class Numbers Divisible by Three, Five or by Seven
- Rational points on quadratic twists of an elliptic curve :4F#FF ElKLBg!&M}
- AG?tDjM}0l5$Rj@. #
- ?7HG AG?t$O ``$$$/$D'' $"$k$+ # 1 $O$8$a$K
- k , l , E k l k-T0 . , v k , ,
- The Behavior of MordellWeil Groups under Field Extensions
- ON THE CLASS NUMBERS OF CERTAIN NUMBER FIELDS OBTAINED FROM POINTS ON ELLIPTIC CURVES
- Counting Rational Points on Projective Space with Certain Congruent Conditions
- [1] E. ( ), , , 1974. [2] , , 9, , 1987.
- [1] E. ( ), , , 1974. [2] , , 9, , 1987.
- [1] E. ( ), , , 1974. [2] , , 9, , 1987.
- [1] L. V. ( ), , , 1982. [2] , ( 3 ), , 1961.
- x , x (x) . , (x) x/ log x . 1896 Hadamard
- RATIONAL POINTS ON QUADRATIC TWISTS OF AN ELLIPTIC CURVE
- f(x + y) = f(x) + f(y), f(tx) = tf(x) 2.1 A (m, n) , x An
- On the reduction of certain isogenies of elliptic curves via the formulas by Velu
- [1] , --( ), , 2010. [2] D. Cox, J. Little, D. O'Shea ( ),
- [ ] , --Linear Algebra, , 2004. [ 1] , , 1, , 1974.
- (Atsushi SATO) 2 a, b , X 3 F(a, b ; X)
- :4F# FF(Atsushi SATO) 2001 G/EY8e4--
- DISTRIBUTION OF RATIONAL POINTS ON CERTAIN ALGEBRAIC SURFACES
- 1234 " " " " , 1, 2, 3, 4 1234
- [1] L. V. ( ), , , 1982. [2] , ( 3 ), , 1961.
- Rational points on quadratic twists of an elliptic curve :4F# FF ElKLBg!&M
- DISTRIBUTION OF RATIONAL POINTS ON CERTAIN ALGEBRAIC SURFACES
- The Behavior of Mordell-Weil Groups under Field Extensions
- DISTRIBUTION OF RATIONAL POINTS ON CERTAIN ALGEBRAIC SURFACES
- ##### III ## ## # (Atsushi SATO)*
- ##### B ## 2010 ####
- ##### III ## # (Atsushi SATO)*
- RATIONAL POINTS ON QUADRATIC TWISTS OF AN ELLIPTIC CURVE
- ##### C ## 2009 ####
- Counting Rational Points on Projective Space with Certain Congruent Conditions
- The Behavior of Mordell-Weil Groups under Field Extensions
- ##### C ## 2006 ####
- Construction of Number Fields of Odd Degree with Class Numbers Divisible by Three, Five or by Seven
- ############## Batyrev-Manin #### ############ ## # (Atsushi Sato)
- ### 5 #############* ### # # ## # (Atsushi SATO)
- Construction of Number Fields of Odd Degree with Class Numbers Divisible by Three, Five or by Seven
- On the class numbers of certain number fields obtained from points on elliptic curves III
- On the class numbers of certain number fields obtained from points on elliptic curves III #
- [1] D. / J. / D. ( / / / / ), [2] , ----, , , 1987.
- ## #y ######, #######################, 1OUNIX ###### 2O###
- ON THE CLASS NUMBERS OF CERTAIN NUMBER FIELDS OBTAINED FROM POINTS ON ELLIPTIC CURVES
- ##### B ## 2008 ####
- On the class numbers of certain number fields obtained from points on elliptic curves III*
- ##### B ## 2007 ####
- ON THE CLASS NUMBERS OF CERTAIN NUMBER FIELDS OBTAINED FROM POINTS ON ELLIPTIC CURVES II*
- k ####, l #####, E # k ######### l # k-### T0 ### ########. ##, v # k ##############, #####, #
- On the reduction of certain isogenies of elliptic curves via the formulas by Velu #
- [1] L. V. ( ), , , 1982. [2] , ( 3 ), , 1961.
- ON THE CLASS NUMBERS OF CERTAIN NUMBER FIELDS OBTAINED FROM POINTS ON ELLIPTIC CURVES
- Batyrev-Manin (Atsushi Sato)
- ##### A ## 2006 ####
- ##### B ## 2004 ####
- ##### A ## 2004 ####
- ##### II ## ## # (Atsushi SATO)*
- On the reduction of certain isogenies of elliptic curves via the formulas by V'elu *
- ##### C ## 2005 ####
- ## #y ## x ###, x ######### ss(x) ###. ####, ss(x) ##### x= logx
- 2 #### ## #y
- A = (aij) n , Aij A (i, j) , (i, j) Aji n A := (Aji) = t
- W = { 0 } An , W = a1, a2, . . . , ar 1 a1, a2, . . . , ar
- W , x, y W x + y W, tx W
- , K R C , K . -1 y (x, y ) x, y Re z, Im z ,
- ##### B ## 2011 ####
- 15.3 , 14.3 ( ) A . , E.1 2 Jordan
- f , df , f ( ) . , ( ) 1 g1 df1 + g2 df2 + + gn dfn 1 .
- (E-mail: atsushi@math.tohoku.ac.jp) [1] , --Linear Algebra, , 2004.
- 14, 15 . K , A 14.3 ( )
- K = R . , , , . x1, x2, . . . , xn ( ) 2
- f, g df, dg , df dg , df, dg ( ) . , 1 h1 df1 dg1 + h2 df2 dg2 + + hn dfn dgn+ 2
- x1 x2 . . . xn P x1, x2, . . . , xn
