.\" DO NOT MODIFY THIS FILE!  It was generated by help2man 1.36.
.TH LCALC "1" "May 2008" "lcalc 1.11 Feb 5, 2008" "User Commands"
.SH NAME
lcalc \- program for calculating with L-functions
.SH SYNOPSIS
.B lcalc
[\fIOPTIONS\fR]...
.SH DESCRIPTION
lcalc 1.11 Feb 5, 2008
.PP
This program computes zeros and values of L\-function.
.TP
\fB\-h\fR, \fB\-\-help\fR
Print help and exit
.TP
\fB\-V\fR, \fB\-\-version\fR
Print version and exit
.TP
\fB\-v\fR, \fB\-\-value\fR
compute L\-function at x+iy. Should be used in
conjuction with x and y options
(default=off)
.TP
\fB\-x\fR, \fB\-\-x\fR=\fIDouble\fR
Used with value,value\-line\-segment, and
zeros\-interval options  (default=`.5')
.TP
\fB\-y\fR, \fB\-\-y\fR=\fIDouble\fR
Used with value,value\-line\-segment, and
zeros\-interval options  (default=`0')
.TP
\fB\-\-value\-file\fR=\fIfilename\fR
compute L\-function at points specified in file
.TP
\fB\-\-value\-line\-segment\fR
compute L\-function along a line segment
connecting (x,y) to (X,Y) at number\-sample
points  (default=off)
.TP
\fB\-X\fR, \fB\-\-X\fR=\fIDouble\fR
Used with value\-line\-segment  (default=`.5')
.TP
\fB\-Y\fR, \fB\-\-Y\fR=\fIDouble\fR
Used with value\-line\-segment  (default=`100')
.TP
\fB\-n\fR, \fB\-\-number\-samples\fR=\fIINT\fR
Used with value\-line\-segment, and interpolate
options  (default=`1000')
.TP
\fB\-z\fR, \fB\-\-zeros\fR=\fIINT\fR
number of zeros to find
.TP
\fB\-Z\fR, \fB\-\-zeros\-interval\fR
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)
.TP
\fB\-\-stepsize\fR=\fIDouble\fR
Used with zeros\-interval
.TP
\fB\-d\fR, \fB\-\-derivative\fR=\fIINT\fR
compute derivative. use \fB\-d\fR \fB\-1\fR to specify
logarithmic derivative.
.TP
\fB\-e\fR, \fB\-\-elliptic\-curve\fR
specify an elliptic curve over Q. Use with the
a1 a2 a3 a4 a6 options  (default=off)
.TP
\fB\-\-a1\fR=\fIrational_number\fR
Used with the elliptic\-curve option
.TP
\fB\-\-a2\fR=\fIrational_number\fR
Used with the elliptic\-curve option
.TP
\fB\-\-a3\fR=\fIrational_number\fR
Used with the elliptic\-curve option
.TP
\fB\-\-a4\fR=\fIrational_number\fR
Used with the elliptic\-curve option
.TP
\fB\-\-a6\fR=\fIrational_number\fR
Used with the elliptic\-curve option
.TP
\fB\-F\fR, \fB\-\-file\-input\fR=\fIfilename\fR
input a file with basic L\-function data
.TP
\fB\-u\fR, \fB\-\-url\fR=\fIurl\fR
input a web based file with basic L\-function
data. Specify the url of the file
.TP
\fB\-i\fR, \fB\-\-interpolate\fR=\fIfilename2\fR
interpolate between two L\-functions and find
their zeros. Should be used in conjunction
with file\-input
.TP
\fB\-C\fR, \fB\-\-output\-character\fR=\fISTRING\fR if twisting, output the character
(possible
values="1", "2" default=`1')
.TP
\fB\-o\fR, \fB\-\-output\-data\fR=\fInumber\fR Dirichlet coeffs
output basic data for the underlying L\-function
.IP
(default=`10')
.TP
\fB\-\-verbose\fR=\fIINT\fR
verbosity > 0 outputs extra info  (default=`0')
.TP
\fB\-P\fR, \fB\-\-precision\fR=\fIINT\fR
number digits precision  (default=`14')
.TP
\fB\-S\fR, \fB\-\-sacrifice\fR=\fIINT\fR
number digits to sacrifice  (default=`2')
.TP
\fB\-r\fR, \fB\-\-rank\-compute\fR
compute the rank  (default=off)
.TP
\fB\-\-rank\-verify\fR=\fIINT\fR
verify if specified rank is correct
.TP
\fB\-l\fR, \fB\-\-rank\-limit\fR=\fIINT\fR
when doing quadratic twists limit to
L\-functions with specified rank
.TP
\fB\-t\fR, \fB\-\-tau\fR
Ramanujan tau L\-function (weight 12, full
level)  (default=off)
.TP
\fB\-q\fR, \fB\-\-twist\-quadratic\fR
twist by fundamental quadratic characters,
start <= discriminant <= finish. Use with
start and finish options.  (default=off)
.TP
\fB\-s\fR, \fB\-\-start\fR=\fIinteger\fR
Used with various twisting options
.TP
\fB\-f\fR, \fB\-\-finish\fR=\fIinteger\fR
Used with various twisting options. Default has
finish=start
.TP
\fB\-\-twist\-quadratic\-even\fR
twist by fundamental quadratic characters, even
functional eqn, start <= discriminant <=
finish  (default=off)
.TP
\fB\-p\fR, \fB\-\-twist\-primitive\fR
twist by all primitive Dirichlet characters
with start <= conductor <= finish. For
L\-functions with complex Dirichlet
coefficients, conjugate characters are
considered equaivalent  (default=off)
.TP
\fB\-A\fR, \fB\-\-twist\-all\fR
twist by all Dirichlet characters with start <=
conductor <= finish.  (default=off)
.TP
\fB\-a\fR, \fB\-\-twist\-all\-no\-conj\-pairs\fR twist by all Dirichlet characters with start <=
conductor <= finish. For L\-functions with
complex Dirichlet coefficients, conjugate
pairs of characters are considered equivalent
.IP
(default=off)
.TP
\fB\-c\fR, \fB\-\-twist\-complex\-no\-conj\-pairs\fR
twist by all complex primitive Dirichlet
.IP
characters with start <= conductor <= finish.
For L\-functions with complex Dirichlet
coefficients, conjugate pairs of characters
are considered equivalent  (default=off)
.TP
\fB\-g\fR, \fB\-\-twist\-generic\fR
twist by a generic complex Dirichlet characters
with start <= conductor <= finish.
(default=off)
.TP
\fB\-D\fR, \fB\-\-degree\fR=\fIdegree\fR
can only be used in conjuction with
twist\-primitive (?). Select characters of
specified degree. Not yet implemented
.SH "SEE ALSO"
The full documentation for
.B lcalc
is maintained as a Texinfo manual.  If the
.B info
and
.B lcalc
programs are properly installed at your site, the command
.IP
.B info lcalc
.PP
should give you access to the complete manual.