/usr/include/Lfunction/Lnumberzeros.h is in liblfunction-dev 1.23+dfsg-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | /*
Copyright (C) 2001,2002,2003,2004 Michael Rubinstein
This file is part of the L-function package L.
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
Check the License for details. You should have received a copy of it, along
with the package; see the file 'COPYING'. If not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
//Computes N(T) without S(T) and to within O(1/T)
//(N(T) is the number of zeros in the critical strip with |t|<T)
template <class ttype>
Double L_function <ttype>::
N(Double T)
{
Double x;
int i;
x=T*log(Q)*2/Pi; //contribution from the conductor
//contribution from the gamma factors
for(i=1;i<=a;i++){
x=x+imag(log_GAMMA( (.5+I*T)*gamma[i]+lambda[i] )
-log_GAMMA( (.5-I*T)*gamma[i]+lambda[i] )) /Pi;
}
// contribution from the pole at s=1 if there is one
// (actually considers poles on the line Re_s=1)
for(i=1;i<=number_of_poles;i++)
if(real(pole[i])>-10E-7&&real(pole[i])<1+10E-7) x=x+1;
return x;
}
|