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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.

Print help and exit
Print version and exit
compute L-function at x+iy. Should be used in conjunction with x and y options (default=off)
Used with value,value-line-segment, and zeros-interval options (default=`.5')
Used with value,value-line-segment, and zeros-interval options (default=`0')
compute L-function at points specified in file
compute L-function along a line segment connecting (x,y) to (X,Y) at number-sample points (default=off)
Used with value-line-segment (default=`.5')
Used with value-line-segment (default=`100')
Used with value-line-segment, and interpolate options (default=`1000')
number of zeros to find
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)
Used with zeros-interval
compute derivative. use -d -1 to specify logarithmic derivative.
specify an elliptic curve over Q. Use with the a1 a2 a3 a4 a6 options (default=off)
Used with the elliptic-curve option
Used with the elliptic-curve option
Used with the elliptic-curve option
Used with the elliptic-curve option
Used with the elliptic-curve option
input a file with basic L-function data
input a web based file with basic L-function data. Specify the url of the file
interpolate between two L-functions and find their zeros. Should be used in conjunction with file-input
(possible values="1", "2" default=`1')
output basic data for the underlying L-function
(default=`10')
verbosity > 0 outputs extra info (default=`0')
number digits precision (default=`14')
number digits to sacrifice (default=`2')
compute the rank (default=off)
verify if specified rank is correct
when doing quadratic twists limit to L-functions with specified rank
Ramanujan tau L-function (weight 12, full level) (default=off)
twist by fundamental quadratic characters, start <= discriminant <= finish. Use with start and finish options. (default=off)
Used with various twisting options
Used with various twisting options. Default has finish=start
twist by fundamental quadratic characters, even functional eqn, start <= discriminant <= finish (default=off)
twist by all primitive Dirichlet characters with start <= conductor <= finish. For L-functions with complex Dirichlet coefficients, conjugate characters are considered equaivalent (default=off)
twist by all Dirichlet characters with start <= conductor <= finish. (default=off)
conductor <= finish. For L-functions with complex Dirichlet coefficients, conjugate pairs of characters are considered equivalent
(default=off)
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)
twist by a generic complex Dirichlet characters with start <= conductor <= finish. (default=off)
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.

May 2008 lcalc 1.11 Feb 5, 2008