文摘
It is known that the Riemann hypothesis holds if and only if the function 16d394e2a06481259d71c17b" title="Click to view the MathML source">χ(0,1) can be approximated by linear combinations of uα in L2(0,1). Here d70d99d" title="Click to view the MathML source">uα(x) is defined by [α/x]−α[1/x] for 0<α<1. In this note we generalize the Beurling's equivalent condition by replacing the function 16d394e2a06481259d71c17b" title="Click to view the MathML source">χ(0,1) with χ(a,b) for any 0≤a<b≤1.