DIRICHLET SERIES SATISFYING A RIEMANN TYPE FUNCTIONAL EQUATION AND SHARING A SET

In 2011, Li [9] proved that if two L-functions L-1 and L-2 satisfy the same functional equation with a(1) = 1 and L-1(-1) (cj) = L-2(-1) (cj) for two finite distinct complex numbers c(1) and c(2), then L-1 = L-2. We prove that if two L-functions L-1 and L-2 satisfy the same functional equation with a(1) = 1 and EL1(S) = EL2(S) for a finite set S = {c(1), c(2)}, where c(1) and c(2) are two finite distinct complex values, then L-1 = L-2.