Dedekind Sums
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02-26-2024, 02:28 PM
Post: #1
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Dedekind Sums
Definition
The Dedekind Sum is defined as follows: Let P and Q be relatively prime integers, that is GCD(P, Q) = 1. Then S is the Dedekind sum as: S = Σ( ((I ÷ Q)) × ((P × I ÷ Q)), for I=1 to Q) The double parenthesis around the terms I ÷ Q and P × I ÷ Q signify a custom function: (( X )) = 0, if X is an integer X – FLOOR(X) – 1/2, if X is not an integer If X is positive, X – INTG(X) – 1/2 HP Prime: DEDEKIND Code: EXPORT DEDEKIND(p,q) P = 2, Q = 17: 0.4705882353 P =14, Q = 57: -0.8187134503 Sources Shipp, R. Dale. “Table of Dedekind Sums” Journal of Research of the National Bureau of Standards-B. Mathematics and Mathematical Physics Vol. 69B, No 4, October-December 1965 https://nvlpubs.nist.gov/nistpubs/jres/6...59_A1b.pdf Retrieved February 21, 2024 Weisstein, Eric W. "Dedekind Sum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DedekindSum.html Retrieved February 18, 2024 |
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Dedekind Sums - Eddie W. Shore - 02-26-2024 02:28 PM
RE: Dedekind Sums - johnb - 02-26-2024, 09:47 PM
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