Provided by: lcalc_1.23+dfsg-11build1_amd64

#### 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)

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   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

#### SEEALSO

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