A note on the zeroes of the Fredholm series

  • Umberto Zannier

    Scuola Normale Superiore, Pisa, Italy
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Abstract

The issue had been raised whether the function $z + z^2 + \cdots + z^{2n}, sometimes called Fredholm series, has infinitely many zeroes in the unit disk. We provide an affirmative answer, proving that in fact every complex number occurs as a value infinitely many times, even restricting the function to any open set meeting the unit circle.

Cite this article

Umberto Zannier, A note on the zeroes of the Fredholm series. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 4, pp. 651–666

DOI 10.4171/RLM/909