Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claims
1927_01_01_biernacki: Biernacki proves that an entire gap series whose exponents have a convergent reciprocal sum takes every value infinitely often, a subclass of Problem 517 of any order; the venue's refereeing is not shown.
1929_12_01_polya: Pólya proves that an entire function of finite order whose exponent gaps are unbounded takes every value infinitely often, which settles the finite-order case of Problem 517; refereed in Math. Z.
1983_01_01_murai: Murai proves that an entire function whose exponents have a convergent reciprocal sum has no finite deficient value, so it takes every value infinitely often; refereed in Ann. Inst. Fourier.