1LCALC(1)                         User Commands                        LCALC(1)
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NAME

6       lcalc - program for calculating with L-functions
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SYNOPSIS

9       lcalc [OPTIONS]...
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DESCRIPTION

12       lcalc 1.11 Feb 5, 2008
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14       This program computes zeros and values of L-function.
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16       -h, --help
17              Print help and exit
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19       -V, --version
20              Print version and exit
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22       -v, --value
23              compute  L-function at x+iy. Should be used in conjuction with x
24              and y options (default=off)
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26       -x, --x=Double
27              Used with value,value-line-segment, and  zeros-interval  options
28              (default=`.5')
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30       -y, --y=Double
31              Used  with  value,value-line-segment, and zeros-interval options
32              (default=`0')
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34       --value-file=filename
35              compute L-function at points specified in file
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37       --value-line-segment
38              compute L-function along a  line  segment  connecting  (x,y)  to
39              (X,Y) at number-sample points  (default=off)
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41       -X, --X=Double
42              Used with value-line-segment  (default=`.5')
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44       -Y, --Y=Double
45              Used with value-line-segment  (default=`100')
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47       -n, --number-samples=INT
48              Used    with   value-line-segment,   and   interpolate   options
49              (default=`1000')
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51       -z, --zeros=INT
52              number of zeros to find
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54       -Z, --zeros-interval
55              number of zeros to find in  an  interval  (1/2+ix,1/2+iy)  using
56              steps  of size stepsize.  Use with the x,y, and stepsize options
57              (default=off)
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59       --stepsize=Double
60              Used with zeros-interval
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62       -d, --derivative=INT
63              compute derivative. use -d -1 to specify logarithmic derivative.
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65       -e, --elliptic-curve
66              specify an elliptic curve over Q. Use with the a1 a2  a3  a4  a6
67              options  (default=off)
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69       --a1=rational_number
70              Used with the elliptic-curve option
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72       --a2=rational_number
73              Used with the elliptic-curve option
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75       --a3=rational_number
76              Used with the elliptic-curve option
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78       --a4=rational_number
79              Used with the elliptic-curve option
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81       --a6=rational_number
82              Used with the elliptic-curve option
83
84       -F, --file-input=filename
85              input a file with basic L-function data
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87       -u, --url=url
88              input  a  web based file with basic L-function data. Specify the
89              url of the file
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91       -i, --interpolate=filename2
92              interpolate between two L-functions and find their zeros. Should
93              be used in conjunction with file-input
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95       -C, --output-character=STRING if twisting, output the character
96              (possible values="1", "2" default=`1')
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98       -o, --output-data=number Dirichlet coeffs
99              output basic data for the underlying L-function
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101              (default=`10')
102
103       --verbose=INT
104              verbosity > 0 outputs extra info  (default=`0')
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106       -P, --precision=INT
107              number digits precision  (default=`14')
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109       -S, --sacrifice=INT
110              number digits to sacrifice  (default=`2')
111
112       -r, --rank-compute
113              compute the rank  (default=off)
114
115       --rank-verify=INT
116              verify if specified rank is correct
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118       -l, --rank-limit=INT
119              when  doing quadratic twists limit to L-functions with specified
120              rank
121
122       -t, --tau
123              Ramanujan tau L-function (weight 12, full level)  (default=off)
124
125       -q, --twist-quadratic
126              twist by fundamental quadratic characters, start <= discriminant
127              <= finish. Use with start and finish options.  (default=off)
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129       -s, --start=integer
130              Used with various twisting options
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132       -f, --finish=integer
133              Used with various twisting options. Default has finish=start
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135       --twist-quadratic-even
136              twist  by fundamental quadratic characters, even functional eqn,
137              start <= discriminant <= finish  (default=off)
138
139       -p, --twist-primitive
140              twist by all primitive Dirichlet characters with start  <=  con‐
141              ductor <= finish. For L-functions with complex Dirichlet coeffi‐
142              cients,  conjugate   characters   are   considered   equaivalent
143              (default=off)
144
145       -A, --twist-all
146              twist  by  all  Dirichlet  characters with start <= conductor <=
147              finish.  (default=off)
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149       -a, --twist-all-no-conj-pairs twist by all  Dirichlet  characters  with
150       start <=
151              conductor  <=  finish.  For  L-functions  with complex Dirichlet
152              coefficients,  conjugate  pairs  of  characters  are  considered
153              equivalent
154
155              (default=off)
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157       -c, --twist-complex-no-conj-pairs
158              twist by all complex primitive Dirichlet
159
160              characters  with  start <= conductor <= finish.  For L-functions
161              with complex Dirichlet coefficients, conjugate pairs of  charac‐
162              ters are considered equivalent  (default=off)
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164       -g, --twist-generic
165              twist  by  a  generic complex Dirichlet characters with start <=
166              conductor <= finish.  (default=off)
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168       -D, --degree=degree
169              can only be used in conjuction with twist-primitive (?).  Select
170              characters of specified degree. Not yet implemented
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174lcalc 1.11 Feb 5, 2008             May 2008                           LCALC(1)