The issue had been raised whether the function z + z^(2) + . . . + z^(2^n) + . . ., 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.
A note on the zeroes of the Fredholm series
Veneziano, F
2020-01-01
Abstract
The issue had been raised whether the function z + z^(2) + . . . + z^(2^n) + . . ., 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.
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