lcalc - program for calculating with L-functions
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
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.