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The Pjateckii-Sapiro prime number theorem. (English) Zbl 0513.10042


MSC:

11N13 Primes in congruence classes
11L40 Estimates on character sums
11N05 Distribution of primes
11B83 Special sequences and polynomials
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References:

[1] Deshouillers, J.-M., Nombres premiers de la forme \([n^c]\), C. R. Acad. Sci. Par. Sér. A-B, 282, 3, A131-A133 (1976) · Zbl 0319.10053
[2] Kolesnik, G. A., The distribution of primes in sequences of the form \([n^c]\), Mat. Zametki, 2, 2, 117-128 (1972) · Zbl 0199.08904
[3] Leitmann, D., Abschätzung trigonometrischer Summen, J. Reine Angew. Math., 317, 209-219 (1980) · Zbl 0421.10024
[4] Phillips, E., The zeta-function of Riemann; Further developments of van der Corput’s method, Quart. J. Math. Oxford, 4, 209-225 (1933) · JFM 59.0204.01
[5] Pjateckiĭ-Sapiro, I. I., On the distribution of prime numbers in sequences of the form \([f(n)]\), Mat. Sb., 33, 559-566 (1953) · Zbl 0053.02702
[6] Titchmarsh, E. C., (The Theory of the Riemann Zeta-Function (1951), Oxford Univ. Press: Oxford Univ. Press London/New York, Oxford) · Zbl 0042.07901
[7] Vaughan, R. C., (On the Estimation of Trigonometrical Sums over Primes, and Related Questions (1977), Institut Mittag-Leffler), Report No. 9
[8] Vinogradov, I. M., The method of Trigonometrical Sums in the Theory of Numbers (1954), Interscience: Interscience London, translated from the Russian, revised and annotated by K. F. Roth and A. Davenport · Zbl 0055.27504
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