HOW IT WORKS a) description file Kummer_main.c: (C program) input: an odd prime q (it is checked that q is prime and odd) output: file primroot.res: first line q; econd line g, a primitive root mod q b) run the main program ./Kummer_main.exe give it an odd prime; the output is the file primroot.res whics contatins a q in the firs line and g a primitive root mod q, in the second line c) FINAL FFT computations using the programs (fftw need to be installed) c1) Kummer-bernoulli-fftwl.c: use the fftw library (long double precision) guru64 interface. Uses the generalised Bernoulli numbers; generating sequence is decimated in frequency. input: files primroot.res. output: K(q) c2) Kummer-psi-fftwl.c: use the fftw library (long double precision) guru64 interface. Uses the psi function of GSL;; generating sequence is decimated in frequency. input: files primroot.res. output: K(q) compiling instructions: Linux (fftw installed using apt-get) ./compile-optiplex-fft.sh /*using long double precision */ gcc -o Kummer-bernoulli-fftwl.exe Kummer-bernoulli-fftwl.c -lfftw3l -lm gcc -o Kummer-psi-fftwl.exe Kummer-psi-fftwl.c -lfftw3l -lgsl -lgslcblas -lm