Autour d'un théorème de Piatetski-Shapiro : nombres premiers dans la suite partie entière de [ n c ]
Thèses d'Orsay, no. 326 (1992) , 114 p. 
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     title = {Autour d'un th\'eor\`eme de {Piatetski-Shapiro} : nombres premiers dans la suite partie enti\`ere de $[n^c]$},
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     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {326},
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Rivat, Joël. Autour d'un théorème de Piatetski-Shapiro : nombres premiers dans la suite partie entière de $[n^c]$. Thèses d'Orsay, no. 326 (1992), 114 p. http://numdam.org/item/BJHTUP11_1992__0326__P0_0/

[1] A. Balog. On the fractional part of p θ . Arch. Math., 40 : 434-440, 1983. | MR | Zbl

[2] A. Balog. On the distribution of p θ mod 1 . Acta Mathematica Hungarica, 35 : 179-199, 1985. | MR | Zbl

[3] A. Balog and J. Friedlander. A Hybrid of Theorems of Vinogradov and Piatetski-Shapiro. to appear, 1990. | MR | Zbl

[4] E. Bombieri and H. Iwaniec. On the Order of ξ ( 1 2 + i t ) . Annali Scuola Norm. Sup. Pisa, 13(3) : 449-472, 1986. | MR | Zbl | Numdam

[5] J.-M. Deshouillers. Propriétés additives et arithmétiques de suites à croissance polynômiale. Thèse de Doctorat, Université de Paris VI, 1972.

[6] J.-M. Deshouillers. Problème de Waring avec exposants non entiers. Bulletin Société mathématique de France, 101 : 285-295, 1973. | MR | Zbl | Numdam | DOI

[7] J.-M. Deshouillers. Un problème binaire en théorie additive. Acta Arithmetica, 25 : 393-403, 1974. | MR | Zbl

[8] J.-M. Deshouillers. Nombres premiers de la forme [nc]. Comptes Rendus de l'Académie des Sciences de Paris Séries A-B, 282(3) : A131-A133, 1976. | MR | Zbl

[9] E. Fouvry and H. Iwaniec. Exponential Sums with Monomials. Journal of Number Theory, 33(3) : 311-333, Nov. 1989. | MR | Zbl | DOI

[10] S. Graham. An algorithm for computing optimal exponent pairs. J. London Math. Soc., 33(2) : 203-218, Apr. 1986. | MR | Zbl | DOI

[11] S. Graham and G. Kolesnik. Van der corput's Method of Exponential Sums, volume 126. Cambridge University Press, Lecture Note Series, 1991. | MR | Zbl

[12] G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. Oxford Science Publications, 1938. | Zbl

[13] G. Harman. Fractional and integral parts of p λ . Acta Arithmetica, 58(2) : 141-152, 1991. | MR | Zbl

[14] D. R. Heath-Brown. Prime numbers in short intervals and a generalized Vaughan identity. Can.J.Math., 34(6) : 1365-1377, Dec. 1982. | MR | Zbl | DOI

[15] D. R. Heath-Brown. The Piatetski-Shapiro Prime Number Theorem. Journal of Number Theory, 16 : 242-266, Apr. 1983. | MR | Zbl | DOI

[16] L. Hong-Quan and J. Rivat. On the Piatetski-Shapiro Prime Number Theorem. preprint, 1990.

[17] M. Huxley and N. Watt. Exponential Sums and the Riemann zeta function. Proceedings London Math. Soc., 53(1) : 1-24, July 1988. | MR | Zbl

[18] H. Iwaniec. A new form of the error term in the linear sieve. Acta Arithmetica, 37(1) : 307-320, 1980. | MR | Zbl

[19] G. Kolesnik. The distribution of primes in sequences of the form [nc]. Mat. Zametki, 2(2) : 117- 128, 1972. | MR | Zbl

[20] G. Kolesnik. Primes of the form [nc]. Pacific J. Math., 118(2) : 437-447, 1985. | MR | Zbl | DOI

[21] D. Leitmann. Durchschnitte von Piatetski-Shapiro Folgen. Monatshefte für Mathematik, 94 : 33-44, 1982. | MR | Zbl

[22] D. Leitmann and D. Wolke. Primzahlen de Gestalt [f(n)]. Math. Z., 145 :81-92, 1975. | MR | Zbl | DOI

[23] E. Phillips. The zeta-function of Riemann ; Further developments of van der Corput's method. Quart. J. Math. Oxford, 4(1) : 209-225, 1933. | Zbl | JFM | DOI

[24] I. Piatetski-Shapiro. On the distribution of prime numbers in sequences of the form [f(n)]. Math. Sbornik, 33(1) : 559-566, 1933. | MR | Zbl

[25] G. Srinivasan. On the number of Abelian groups of a given order. Acta Arithmetica, 23 : 195-205, 1973. | MR | Zbl | DOI

[26] G. Tenenbaum. Introduction à la théorie analytique et probabiliste des nombres. Institut Elie Cartan, Université de Nancy I, 1990. | Zbl

[27] E. C. Titchmarsh. The Theory of Functions. Oxford University Press, 1932. | Zbl | JFM

[28] E. C. Titchmarsh. The Theory of the Riemann Zeta-function, revised by D.R. Heath-Brown. Oxford Science Publications, second edition, 1986. | Zbl | MR

[29] J. Van Der Corput. Zahlentheoretische Abschäzungen. M.A., 84 : 53-79, 1921. | MR | JFM

[30] J. Van Der Corput. Verschärfung der Abschäzung beim Teilerproblem. M.A., 87 : 39-65, 1922. | MR | JFM

[31] R. Vaughan. The Hardy-Littlewood Method. Cambridge University Press, 1981. | MR | Zbl

[32] I. Vinogradov. Representation of an odd number as the sum of three primes. Dokl. Akad. Nauk SSSR, 15 : 291-294, 1937. | JFM | Zbl

[33] I. Vinogradov. Selected Works. Springer Verlag, 1985. | MR | Zbl

[34] E. Whittaker and G. Watson. A course of modem analysis. Cambridge University Press, 1962. | Zbl | MR