In his 1950 thesis [
MR 12,108g], B. Nyman, a student of A. Beurling, proved that the Riemann Hypothesis is equaivalent to the assertion that
is dense in
is the space of functions
Beurling [ MR 17,15a] proved that the following three statements regarding a number with are equivalent:
(1) has nozeros in
(2) is dense in (3) The characteristic function is in the closure of in
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