Tauberian Theorem of Erdős Revisited

Dedicated to the memory of Paul Erdős

In connection with the elementary proof of the prime number theorem, Erdős obtained a striking quadratic Tauberian theorem for sequences. Somewhat later, Siegel indicated in a letter how a powerful "fundamental relation" could be used to simplify the difficult combinatorial proof. Here the author presents his version of the (unpublished) Erdős–Siegel proof. Related Tauberian results by the author are described.

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Received December 20, 1999

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Korevaar, J. Tauberian Theorem of Erdős Revisited. Combinatorica 21, 239–250 (2001). https://doi.org/10.1007/s004930100022

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  • AMS Subject Classification (2000) Classes:  40E05; 11A41