Gaussian primes

Etienne Fouvry; Henryk Iwaniec

Acta Arithmetica (1997)

  • Volume: 79, Issue: 3, page 249-287
  • ISSN: 0065-1036

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Etienne Fouvry, and Henryk Iwaniec. "Gaussian primes." Acta Arithmetica 79.3 (1997): 249-287. <http://eudml.org/doc/206979>.

@article{EtienneFouvry1997,
author = {Etienne Fouvry, Henryk Iwaniec},
journal = {Acta Arithmetica},
keywords = {prime; Gaussian prime; sieve; estimates for bilinear forms},
language = {eng},
number = {3},
pages = {249-287},
title = {Gaussian primes},
url = {http://eudml.org/doc/206979},
volume = {79},
year = {1997},
}

TY - JOUR
AU - Etienne Fouvry
AU - Henryk Iwaniec
TI - Gaussian primes
JO - Acta Arithmetica
PY - 1997
VL - 79
IS - 3
SP - 249
EP - 287
LA - eng
KW - prime; Gaussian prime; sieve; estimates for bilinear forms
UR - http://eudml.org/doc/206979
ER -

References

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  1. [B1] E. Bombieri, On twin almost primes, Acta Arith. 28 (1975), 177-193; Acta Arith. 28 (1976), 457-461. Zbl0319.10051
  2. [B2] E. Bombieri, The asymptotic sieve, Rend. Accad. Naz. XL (5), 1/2 (1975/76). 
  3. [C] M. Coleman, The Rosser-Iwaniec sieve in number fields, with an application, Acta Arith. 65 (1993), 53-83. Zbl0784.11047
  4. [DH] H. Davenport and H. Halberstam, The values of a trigonometric polynomial at well spaced points, Mathematika 13 (1966), 91-96. Zbl0171.00902
  5. [D] W. Duke, Some problems in multidimensional analytic number theory, Acta Arith. 52 (1989), 203-228. Zbl0631.12008
  6. [DFI] W. Duke, J. Friedlander and H. Iwaniec, Equidistribution of roots of a quadratic congruence to prime moduli, Ann. of Math. 141 (1995), 423-441. Zbl0840.11003
  7. [F] E. Fogels, On the zeros of Hecke's L-functions I, II, III, Acta Arith. 7 (1962), 87-106, 131-147, 225-240. Zbl0100.03801
  8. [FI] J. Friedlander and H. Iwaniec, Bombieri's sieve, in: Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, Progr. Math. 138, Birkhäuser, 1996, 411-430. Zbl0862.11052
  9. [GR] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, London, 1965. 
  10. [H] E. Hecke, Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen II, Math. Z. 6 (1920), 11-51. 
  11. [IR] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer, 1982. Zbl0482.10001
  12. [I] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202. Zbl0435.10029
  13. [J] E. Jacobsthal, Über die Darstellung der Primzahlen der Form 4n+1 als Summe zweier Quadrate, J. Reine Angew. Math. 132 (1907), 238-245. 
  14. [K] J. P. Kubilius, On some problems in geometry of prime numbers, Mat. Sb. 31 (73) (1952), 507-542 (in Russian). Zbl0049.03301
  15. [MV] H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc. (2) 8 (1974), 73-82. Zbl0281.10021
  16. [P] J. Pomykała, Cubic norms represented by quadratic sequences, Colloq. Math. 66 (1994), 283-297. Zbl0814.11044
  17. [R] G. J. Rieger, Über die Summe aus einem Quadrat und einem Primzahlquadrat, J. Reine Angew. Math. 231 (1968), 89-100. Zbl0164.05004
  18. [S] A. Selberg, Lectures on Sieves, Collected Papers, Vol. II, Springer, 1991. 
  19. [V] R. C. Vaughan, Mean value theorems in prime number theory, J. London Math. Soc. 10 (1975), 153-162. Zbl0314.10028

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