Gaussian primes

• Autorzy: Etienne Fouvry , Henryk Iwaniec
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 79
• Numer: 3
• Strony: 249-287

Daty

wydano

1997

otrzymano

1996-11-18

Twórcy

autor

Etienne Fouvry

• Bât. 425 - Mathématique, Université de Paris-Sud, 91405 Orsay Cedex, France

autor

Henryk Iwaniec

• Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.

Bibliografia

• [B1] E. Bombieri, On twin almost primes, Acta Arith. 28 (1975), 177-193; Acta Arith. 28 (1976), 457-461.
• [B2] E. Bombieri, The asymptotic sieve, Rend. Accad. Naz. XL (5), 1/2 (1975/76).
• [C] M. Coleman, The Rosser-Iwaniec sieve in number fields, with an application, Acta Arith. 65 (1993), 53-83.
• [DH] H. Davenport and H. Halberstam, The values of a trigonometric polynomial at well spaced points, Mathematika 13 (1966), 91-96.
• [D] W. Duke, Some problems in multidimensional analytic number theory, Acta Arith. 52 (1989), 203-228.
• [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.
• [F] E. Fogels, On the zeros of Hecke's L-functions I, II, III, Acta Arith. 7 (1962), 87-106, 131-147, 225-240.
• [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.
• [GR] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, London, 1965.
• [H] E. Hecke, Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen II, Math. Z. 6 (1920), 11-51.
• [IR] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer, 1982.
• [I] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202.
• [J] E. Jacobsthal, Über die Darstellung der Primzahlen der Form 4n+1 als Summe zweier Quadrate, J. Reine Angew. Math. 132 (1907), 238-245.
• [K] J. P. Kubilius, On some problems in geometry of prime numbers, Mat. Sb. 31 (73) (1952), 507-542 (in Russian).
• [MV] H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc. (2) 8 (1974), 73-82.
• [P] J. Pomykała, Cubic norms represented by quadratic sequences, Colloq. Math. 66 (1994), 283-297.
• [R] G. J. Rieger, Über die Summe aus einem Quadrat und einem Primzahlquadrat, J. Reine Angew. Math. 231 (1968), 89-100.
• [S] A. Selberg, Lectures on Sieves, Collected Papers, Vol. II, Springer, 1991.
• [V] R. C. Vaughan, Mean value theorems in prime number theory, J. London Math. Soc. 10 (1975), 153-162.