Zeros of normalized combinations of ξ(k)(s) on Re(s)=1/2

We consider functions of the form Fc→,a,T(s)=∑j=0Mcj(−1)jL2jξ(a+2j)(s), with L=log⁡T2π and cj real constants satisfying a certain constraint. We show that as T→∞, the proportion of zeros of Fc→,a,T(s) on the critical line Re(s)=1/2 tends to 1.