L = 1;
lfunan(L, 100)
lfun(L, 2)
lfunzeros(L,30)
\pb 32
ploth(t = 0, 100, lfunhardy(L,t))
L = lfuninit(L, [100]);
ploth(t = 0, 100, lfunhardy(L,t))
\\\\\\\\\\\\\\\\\\\\\\\
L = lfuncreate('x^3-2);
lfun(L, 2)
lfunzeros(L,30)
\pb 32
L = lfuninit(L, [30]);
ploth(t = 0, 30, lfunhardy(L,t))
\\\\\\\\\\\\\\\\\\\\\\\
E = ellinit([0,0,1,-7,6]); L = lfuncreate(E);
lfun(E, 1)
lfun(E, 1, 1)
lfun(E, 1, 2)
lfun(E, 1, 3)
ellanalyticrank(E)
lfunzeros(E,10)
\pb 32
Lbad = lfuninit(E, [1/2, 0, 30]);
lfunhardy(Lbad,10)
L = lfuninit(L, [30]); ploth(t = 0, 30, lfunhardy(L,t))
\\\\\\\\\\\\\\\\\\\\\\\
L=lfungenus2([x^2+x, x^3+x^2+1]);
lfunan(L,15)
L = lfuninit(L, [10]);
lfun(L,1)
lfunzeros(L,9)
ploth(t = 0, 10, lfunhardy(L,t))
\\\\\\\\\\\\\\\\\\\\\\\
lfun(-23, 1)
K = bnfinit(x^2+23); [r1,r2] = K.sign
2^r1*(2*Pi)^r2 * K.no * K.reg / sqrt(abs(K.disc)) / K.tu[1]
G = znstar(100, 1);
G.cyc
chi = [2, 0];
zncharconductor(G,[2,0])
L = lfuncreate([G, chi]);
lfun(L, 1)
L = lfuninit(L, [30]);
ploth(t = 0, 30, lfunhardy(L,t))
\\\\\\\\\\\\\\\\\\\\\\\
K = bnfinit(x^3-7);
G = bnrinit(K, [11, [1]]);
G.cyc
chi = [2]
bnrconductor(G, [2])
L = lfuncreate([G, chi]);
lfun(L, 0)
L = lfuninit(L, [1/2,30]);
lfun(L, 0)
lfun(L, 1)
lfunzeros(L,29)
ploth(t = 0, 30, lfunhardy(L,t))
\\\\\\\\\\\\\\\\\\\\\\\
a(N) = Vec(q * eta(q + O(q^N))^24);
L = lfuncreate([a,0,[0,1],12,1,1]);
lfuncheckfeq(L)
a(8)
mfcoefs(mfDelta(), 8)
\\\\\\\\\\\\\\\\\\\\\\\
P = quadhilbert(-47);
N = nfinit(nfsplitting(P));
G = galoisinit(N);
G.gen
G.orders
L1 = lfunartin(N,G, [[a,0;0,a^-1],[0,1;1,0]], 5);
L2 = lfunartin(N,G, [[a^2,0;0,a^-2],[0,1;1,0]], 5);
s = 1 + x + O(x^10);
lfun(1,s)*lfun(-47,s)*lfun(L1,s)^2*lfun(L2,s)^2 - lfun(N,s)