CCCpppnnnnnn���¥¥¥êêêÆÆÆ¿¿¿mmmûûûmmmKKK888888<<<“““êêꆆ†êêêØØد¯¯KKK1-p •Ûƒê, m ≥ 0ÚN ≥ 1 •�ê"�Λ •˜••2m + 1 �gdZ/pNZ-�§¿�( , ): Λ × Λ → Z/pNZ•˜�{é¡Z/pNZ-V‚5."ùp, “�{” •�´p�N�Λ → HomZ/pNZ(Λ, Z/pNZ),x �→ (x, ·)•Ó�"Á¦8Ü{x ∈ Λ | (x, x) = 0}��ƒ‡ê§Lˆ•p, m, N �¼ê"‰‰‰YYY1éz‡�ê0 ≤ n ≤ N, �Λ(n) := {x ∈ Λ | (x, x) ∈ pnZ/pNZ},§3pnΛ �[£e´-½�. �C(n) := |Λ(n)|. ·‚�8I´OŽC(N). C(0) = |Λ| =p(2m+1)N ´²…�.·‚ÄkŽ˜eC(1). û˜mΛ/pΛ, 'uFp-V‚5/ª( , ) mod p, ´Fp þ�˜‡2m + 1‘šòz��g˜m. w,˜‡�ƒx ∈ Λ/pΛ áuΛ(1)/pΛ �…=�x �•Ý•0.·‚äóéz‡2m + 1 ‘Fp Xê�šòz�g˜mV , •Ý•0 ��ƒ‡ê´p2m. e¡ém Š8B. m = 0 ž´²…�. m > 0 ž, �v1, v2 ∈ V ¦�(v1, v1) = 1, (v2, v2) = −1,…(v1, v2) = 0. �V ′ ´{v1, v2} 3V ¥���Ö˜m, §´˜‡2m − 1 ‘šòz��g˜m. 'uT��©), z‡x ∈ V Œ±�¤x = x1v1 + x2v2 + x′, Ù¥x1, x2 ∈ Fp, x′ ∈ V ′.u´(x, x) = x21 − x22 + (x′, x′). •�OŽ÷v(x, x) = 0 �x ��ƒ‡ê, •Ä±eü«œ¹: e(x′, x′) = 0, K÷vx21 − x22 = 0 �(x1, x2) ∈ F2p �‡ê´2p − 1. e(x′, x′) ̸= 0, K÷vx21 − x22 = −(x′, x′) ̸= 0 �(x1, x2) ∈ F2p �‡ê´p − 1 (Ïp ̸= 2). l�d8Bb�•, •Ý•0 �x ��ƒ‡ê�kp2m−2(2p − 1) + (p2m−1 − p2m−2)(p − 1) = p2m ‡.oƒ, C(1) = p2mp(2m+1)(N−1).˜„/, én ≥ 1, �Λ(n)′ := Λ(n) \ pΛ ±9Λ(n)′′ := Λ(n) ∩ pΛ, ½ÂC(n)′ †C(n)′′ ©O•8ÜΛ(n)′ †Λ(n)′′ ��ƒ‡ê. ·‚äó1. n ≥ 2 ž, Λ(n − 2)/pn−1Λ → Λ(n)′′/pnΛ �¦p N�´V�.2. n ≥ 2 ž, d•¹N�Λ(n)′ → Λ(n − 1)′ p��N�Λ(n)′/pnΛ → Λ(n − 1)′/pn−1Λ ´˜‡p2m-é-1 �N�.1ùü‡äó�y²��‰Ñ, ·‚ÄkddOŽC(n)...
