March 3, 2024 ------------- The files Test-ST.txt and Test-Pinch.txt contain the best values of y given in the Kim-Nguyen manuscript To check the values, run: ./Evaluation-h 100 -y 14 -weight 1 -in Test-ST.txt ./Evaluation-h 100 -y 5 -weight 0 -in Test-Pinch.txt Each file .c or .cpp explains how to compile the source. The programs Evaluation-h and MakeLattice require the data files zeroes.txt, alpha.txt and beta.txt which are numerical values related to zeroes of the Riemann zeta function, and computed with arb To do new experiments: - run MakeLattice to create the Mertens lattice basis - run RoundMatrix to round the lattice basis into an integer basis - reduce the matrix using fplll - run Mertens_Enum to perform lattice enumeration tailored for the Mertens basis - run Extract-h to compute the h values derives from the lattice points The files SR140-130-100-30.B88-ENUM and SR140-130-100-30.B88-ENUM2 are sample files to run Mertens_Enum They contain a BKZ-88 reduced basis together with a target vector The corresponding sample output of Mertens_Enum are SR140-130-100-30.B88-ENUM-1.19.OUT and SR140-130-100-30.B88-ENUM-1.19.OUT2 The files 140-119.IN and 140-119.OUT were produced as follows: - The positive y values from the enumeration are filtered by: cat SR140-130-100-30.B88-ENUM-1.19.OUT* | awk '{ if ($1 > 0) print $1}' > 140-119.IN - Then the h values are derived by: ./Extract-h 100 -y 11754 -nu 130 -nuy 100 -nut 30 -exp 60 -dim 140 -in 140-119.IN -weight 1 > 140-119.OUT In the 9th and 10th columns of 140-119.OUT, one can see the best values of (h,y) obtained To see the ordered list by h value: sort -k9 140-119.OUT