Last update of this webpage (but not article): April 17, 2012.
(previous updates of this page: March 13, 2012)

Maple Package

• HANS
  [Added March 13, 2012: This new version of HANS contains a new procedure, E01s. For the record, here is the old version of HANS]

Sample Input and Output for HANS

• If you want to see the first 700 terms of the sequence C₀₁₁(N) as exact rational numbers, followed by their floating-point renditions, that overwhelmingly shatter Rademacher's conjecture by showing that that sequence does not converge to anything (in particular not to -0.29292754...) but instead eventually oscillates widely getting ever-so-clse to plus infinity and ever-so-close to negative infinity (with a period that seems to be 32), the input gives the output.

• If you want to see the first 500 terms of the sequences C_01j(N) for j from 1 to 10, both in exact rational arithmetic, and in floating-point,
  the input gives the output.

• If you want to see the first 700 terms of the sequence C₁₂₁(N)
  the input gives the output.

• If you want to see the "closest encounters" of the sequences C_hkl(N) to Radmacher's alleged (but wrong!) "limit" (that he called, with wishful thinking, C_hkl(∞)) for 0 ≤ h < k ≤ 3, (gcd(h,k)=1), l ≤5, and N ≤ 250,
  the input gives the output.

• If you want to conduct your own computer experiments with our data, we have put all the 10 sequences C_01j(N) for 1 ≤ j ≤ 10, for 1 ≤ N ≤ 800, into one file, called
  HANSC01,
  in Maple readable format. We named that sequence C01r. For example, C₀₁₇(597) could be gotten (once you uploaded that file), by typing
  C01r[7][597];

• An even larger list then above, put all the 10 sequences C_01j(N) for 1 ≤ j ≤ 10, for 1 ≤ N ≤ 850, into one file, called
  HANSC01a,
  in Maple readable format. We also named that sequence C01r. For example, C₀₁₇(597) could be gotten (once you uploaded that file), by typing
  C01r[7][597];

• If you want even more data, but in floating-point, we put all the 40 sequences C_01j(N) for 1 ≤ j ≤ 40, for 1 ≤ N ≤ 1000, into one file, called
  HANSC01f,
  in Maple readable format. We named that sequence C01f. For example, the floating-point approximation of C₀₁₇(999) could be gotten gotten (once you uploaded that file), by typing
  C01f[7][999];

• If you want to see the 21 sequences C_01(-j)(N) for j from 0 to 20 and 1 ≤ N ≤ 500
  the input yields the output ,
  in Maple readable format. We named that sequence C01Minus. To get C_01(-j)(N), simply type, C01Minus[j+1][N]; For example, C_01(-7)(456) could be gotten (once you uploaded that file), by typing
  C01Minus[8][456];

• If you want to see conjectured (appx.) asymptotic expressions for C_01l(N) for l between 1 and 15,
  the input gives the output.

• If you want to see the values, in floating-point, of C_hkl(N) for 0 < h < k < 10 , k ≥ 3, with gcd(h,k)=1 and for l between 1 and 10, and N between 1 and 400
  the input gives the output.

• [Added March 13, 2012]

  If you want to see the first 1500 terms of the sequence C₀₁₁(N)*(2*N)!,
  the input gives the output.

  [Added April 17, 2012]

  If you want to see the first 2000 terms of the sequence C₀₁₁(N)*(2*N)!,
  the input gives the output.

• [Added March 13, 2012]

  If you want to see conjectured (appx.) asymptotic expressions for C₀₁₁(N) (using 1500 terms rather than 900 as in oHANS10)
  the input gives the output.

  [Added April 17, 2012]

  If you want to see conjectured (appx.) asymptotic expressions for C₀₁₁(N) (using 2000 terms rather than 1500 as in oHANS13)
  the input gives the output.
  [Note the "shifting of the perihelion!", now the maxima are at 1(mod 32) and the minima at 17 (mod 32)]

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