Abstract
As we know, the prime counting function satisfies the asymptotic relation π(x) ~ x/ log x, so that the n-th prime p n is asymptotic to n log n. In order to describe the asymptotic behavior of sequences and functions, one quickly recognized a need for standards of ‘regular growth’. Landau [1911] studied sums, which involve regularly increasing sequences {q n } such as the primes, by comparing them to integrals. Pólya [1917], [1923] extended the results and investigated the counting function for the zeros of entire functions.
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© 2004 Springer-Verlag Berlin Heidelberg
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Korevaar, J. (2004). Karamata’s Heritage: Regular Variation. In: Tauberian Theory. Grundlehren der mathematischen Wissenschaften, vol 329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10225-1_4
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DOI: https://doi.org/10.1007/978-3-662-10225-1_4
Publisher Name: Springer, Berlin, Heidelberg
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