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.

lcalc 1.11 Feb 5, 2008                              May 2008                                            LCALC(1)