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lcalc(1) [debian man page]

LCALC(1)							   User Commands							  LCALC(1)

NAME
lcalc - program for calculating with L-functions SYNOPSIS
lcalc [OPTIONS]... DESCRIPTION
lcalc 1.11 Feb 5, 2008 This program computes zeros and values of L-function. -h, --help Print help and exit -V, --version Print version and exit -v, --value compute L-function at x+iy. Should be used in conjuction with x and y options (default=off) -x, --x=Double Used with value,value-line-segment, and zeros-interval options (default=`.5') -y, --y=Double Used with value,value-line-segment, and zeros-interval options (default=`0') --value-file=filename compute L-function at points specified in file --value-line-segment compute L-function along a line segment connecting (x,y) to (X,Y) at number-sample points (default=off) -X, --X=Double Used with value-line-segment (default=`.5') -Y, --Y=Double Used with value-line-segment (default=`100') -n, --number-samples=INT Used with value-line-segment, and interpolate options (default=`1000') -z, --zeros=INT number of zeros to find -Z, --zeros-interval number of zeros to find in an interval (1/2+ix,1/2+iy) using steps of size stepsize. Use with the x,y, and stepsize options (default=off) --stepsize=Double Used with zeros-interval -d, --derivative=INT compute derivative. use -d -1 to specify logarithmic derivative. -e, --elliptic-curve specify an elliptic curve over Q. Use with the a1 a2 a3 a4 a6 options (default=off) --a1=rational_number Used with the elliptic-curve option --a2=rational_number Used with the elliptic-curve option --a3=rational_number Used with the elliptic-curve option --a4=rational_number Used with the elliptic-curve option --a6=rational_number Used with the elliptic-curve option -F, --file-input=filename input a file with basic L-function data -u, --url=url input a web based file with basic L-function data. Specify the url of the file -i, --interpolate=filename2 interpolate between two L-functions and find their zeros. Should be used in conjunction with file-input -C, --output-character=STRING if twisting, output the character (possible values="1", "2" default=`1') -o, --output-data=number Dirichlet coeffs output basic data for the underlying L-function (default=`10') --verbose=INT verbosity > 0 outputs extra info (default=`0') -P, --precision=INT number digits precision (default=`14') -S, --sacrifice=INT number digits to sacrifice (default=`2') -r, --rank-compute compute the rank (default=off) --rank-verify=INT verify if specified rank is correct -l, --rank-limit=INT when doing quadratic twists limit to L-functions with specified rank -t, --tau Ramanujan tau L-function (weight 12, full level) (default=off) -q, --twist-quadratic twist by fundamental quadratic characters, start <= discriminant <= finish. Use with start and finish options. (default=off) -s, --start=integer Used with various twisting options -f, --finish=integer Used with various twisting options. Default has finish=start --twist-quadratic-even twist by fundamental quadratic characters, even functional eqn, start <= discriminant <= finish (default=off) -p, --twist-primitive twist by all primitive Dirichlet characters with start <= conductor <= finish. For L-functions with complex Dirichlet coefficients, conjugate characters are considered equaivalent (default=off) -A, --twist-all twist by all Dirichlet characters with start <= conductor <= finish. (default=off) -a, --twist-all-no-conj-pairs twist by all Dirichlet characters with start <= conductor <= finish. For L-functions with complex Dirichlet coefficients, conjugate pairs of characters are considered equivalent (default=off) -c, --twist-complex-no-conj-pairs twist by all complex primitive Dirichlet characters with start <= conductor <= finish. For L-functions with complex Dirichlet coefficients, conjugate pairs of characters are considered equivalent (default=off) -g, --twist-generic twist by a generic complex Dirichlet characters with start <= conductor <= finish. (default=off) -D, --degree=degree can only be used in conjuction with twist-primitive (?). Select characters of specified degree. Not yet implemented SEE ALSO
The full documentation for lcalc is maintained as a Texinfo manual. If the info and lcalc programs are properly installed at your site, the command info lcalc should give you access to the complete manual. lcalc 1.11 Feb 5, 2008 May 2008 LCALC(1)
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