#C12.txt, Feb. 26, 2018, Experimental Mathematics (Rutgers), Spring 2018

Help:=proc(): print(`CheckP50L5(A)`): end:

#Checks the <= on p. 50 lines 4-5 of H. Iwaniec's book "Lectures on the Riemann Zeta Function". It is wrong! He probably meant << rather than <=
#If it was right the output should always be <=1
CheckP50L5:=proc(A) local m,n,L,R:
L:=add(add(abs(A[m]*A[n])/(log(m)-log(n))^2,m=1..n-1), n=1..nops(A))+
add(add(abs(A[m]*A[n])/(log(m)-log(n))^2,m=n+1..nops(A)), n=1..nops(A)):

R:=add( abs(A[n])^2*add(m^2/(n-m)^2 ,m=1..n-1),n=1..nops(A)):

evalf(L/R):

end: