170609(2)

Ruby


The Kac-Wakimoto Conjecture(2)

The 1-2-3 of Modular Forms に
載っていない方は、書籍ではなく論文から
探してきた。

def A24(n)
  m = n + 3
  s = 0
  (1..m).each{|b|
    (b + 1..m).each{|a|
      1.step(m, 2){|x|
        1.step(m, 2){|y|
          s += (a * b) ** 3 * (a * a - b * b) ** 2 if a * x + b * y == m
        }
      }
    }
  }
  s / 72
end

def A48(n)
  m = n + 6
  s = 0
  (1..m).each{|c|
    (c + 1..m).each{|b|
      (b + 1..m).each{|a|
        1.step(m, 2){|x|
          1.step(m, 2){|y|
            1.step(m, 2){|z|
              s += (a * b * c) ** 3 * ((a * a - b * b) * (a * a - c * c) * (b * b - c * c)) ** 2 if a * x + b * y + c * z == m
            }
          }
        }
      }
    }
  }
  s / 3110400
end

n = 15
p (0..n).map{|i| A24(i)}
p (0..n).map{|i| A48(i)}

出力結果
[1, 24, 276, 2048, 11178, 48576, 177400, 565248, 1612875, 4200352, 10131156, 22892544, 48897678, 99448320, 193740408, 363315200]
[1, 48, 1128, 17344, 196836, 1764192, 13051008, 82244736, 452197434, 2210431056, 9753024192, 39328459968, 146436844568, 507826976160, 1652238451200, 5074887938688]