no. 3
Trigonometric sums over primes III
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 727-740.

On donne une majoration nouvelle de la somme trigonométrique

∑ P≤p<2P e(αp k )
où k≥5,p désigne un nombre premier et e(x)=exp(2πix).

New bounds are given for the exponential sum

∑ P≤p<2P e(αp k )
were k≥5,p denotes a prime and e(x)=exp(2πix).

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Harman, Glyn. Trigonometric sums over primes III. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 727-740. http://archive.numdam.org/item/JTNB_2003__15_3_727_0/

[1] R.C. Baker, G. Harman, On the distribution of αpk modulo one. Mathematika 38 (1991), 170-184. | Zbl

[2] E. Fouvry, P. Michel, Sur certaines sommes d'exponentielles sur les nombres premiers. Ann. Sci. Ec. Norm. Sup. IV Ser. 31 (1998), 93-130. | Numdam | MR | Zbl

[3] A. Ghosh, The distribution of αp2 modulo one. Proc. London Math. Soc. (3) 42 (1981), 252-269. | Zbl

[4] G. Harman, Trigonometric sums over primes I. Mathematika 28 (1981), 249-254. | MR | Zbl

[5] G. Harman, Trigonometric sums over primes II. Glasgow Math. J. 24 (1983), 23-37. | MR | Zbl

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

[7] K. Kawada, T.D. Wooley, On the Waring-Goldbach problem for fourth and fifth powers. Proc. London Math. Soc. (3) 83 (2001), 1-50. | MR | Zbl

[8] R.C. Vaughan, Mean value theorems in prime number theory. J. London Math. Soc. (2) 10 (1975), 153-162. | MR | Zbl

[9] R.C. Vaughan, The Hardy-Littlewood Method second edition. Cambridge University Press, 1997. | MR | Zbl

[10] I.M. Vinogradov, Some theorems concerning the theory of primes. Rec. Math. Moscow N.S. 2 (1937), 179-194. | JFM | Zbl

[11] I.M. Vinogradov, A new estimation of a trigonometric sum containing primes. Bull. Acad. Sci. URSS Ser. Math. 2 (1938), 1-13. | JFM | Zbl

[12] K.C. Wong, On the distribution of αpk modulo one. Glasgow Math. J. 39 (1997), 121-130. | MR | Zbl

[13] T.D. Wooley, New estimates for Weyl sums. Quart. J. Math. Oxford (2) 46 (1995), 119-127. | MR | Zbl