/* 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; }

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