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 conjunction 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 conjunction 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.