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1993 | 65 | 1 | 53-83
Tytuł artykułu

The Rosser-Iwaniec sieve in number fields, with an application

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
65
Numer
1
Strony
53-83
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-09-07
poprawiono
1993-02-08
Twórcy
  • Department of Mathematics, Umist, P.O. Box 88, Manchester, M60 1QD, England
Bibliografia
  • [1] N. C. Ankeny, Representations of primes by quadratic forms, Amer. J. Math. 74 (1952), 913-919.
  • [2] K. Bulota, On Hecke Z-functions and the distribution of the prime numbers of an imaginary quadratic field, Litovsk. Mat. Sb. 4 (1964), 309-328 (in Russian).
  • [3] M. D. Coleman, The distribution of points at which binary quadratic forms are prime, Proc. London Math. Soc. (3) 61 (1990), 433-456.
  • [4] M. D. Coleman, A zero-free region for the Hecke L-functions, Mathematika 37 (1990), 287-304.
  • [5] M. D. Coleman, The distribution of points at which norm-forms are prime, J. Number Theory 41 (1992), 359-378.
  • [6] P. X. Gallagher, A large sieve density estimate near σ = 1, Invent. Math. 11 (1970), 329-339.
  • [7] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974.
  • [8] D. R. Heath-Brown and H. Iwaniec, On the differences between consecutive primes, Invent. Math. 55 (1979), 49-69.
  • [9] D. R. Heath-Brown and S. J. Patterson, The distribution of Kummer sums at prime arguments, J. Reine Angew. Math. 310 (1979), 111-130.
  • [10] E. Hecke, Eine neue Art von Zeta Functionen und ihre Beziehungen zur Verteilung der Primzahlen, I, II, Math. Z. 1 (1918), 357-376; 6 (1920), 11-51.
  • [11] J. G. Hinz, A generalization of Bombieri's prime number theorem to algebraic number fields, Acta Arith. 51 (1988), 173-193.
  • [12] J. G. Hinz, Chen's theorem in totally real algebraic number fields, Acta Arith. 58 (1991), 335-361.
  • [13] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202.
  • [14] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320.
  • [15] H. Iwaniec and M. Jutila, Primes in short intervals, Ark. Mat. 17 (1979), 167-176.
  • [16] D. Johnson, Mean values of Hecke L-functions, J. Reine Angew. Math. 305 (1979), 195-205.
  • [17] W. B. Jurkat and H.-E. Richert, An improvement of Selberg's sieve method, I, Acta Arith. 11 (1965), 217-240.
  • [18] R. M. Kaufman, Estimate of the Hecke L-function on the half-line, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 91 (1979), 40-51 (in Russian).
  • [19] F. B. Koval'chik, Density theorems and the distribution of primes in sectors and progressions, Dokl. Akad. Nauk SSSR (N.S.) 219 (1974), 31-34 (in Russian).
  • [20] J. P. Kubilius, The decomposition of prime numbers into two squares, Dokl. Akad. Nauk SSSR (N.S.) 77 (1951), 791-794 (in Russian).
  • [21] J. P. Kubilius, On some problems of the geometry of prime numbers, Mat. Sb. (N.S.) 31 (1952), 507-542 (in Russian).
  • [22] J. P. Kubilius, On a problem in the n-dimensional analytic theory of numbers, Viliniaus Valst. Univ. Mokslo dardai Fiz. Chem. Moksly Ser. 4 (1955), 5-43.
  • [23] T. Mitsui, Generalised prime number theorem, Japan. J. Math. 26 (1956), 1-42.
  • [24] R. W. K. Odoni, The distribution of integral and prime-integral values of systems of full-norm polynomials and affine-decomposable polynomials, Mathematika 26 (1979), 80-87.
  • [25] K. Ramachandra, A simple proof of the mean fourth power estimate for ζ(1/2+it) and L(1/2+it,χ), Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1 (1974), 81-97.
  • [26] S. Ricci, Local distribution of primes, Ph.D. thesis, University of Michigan, 1976.
  • [27] H.-E. Richert, Selberg's sieve with weights, Mathematika 16 (1969), 1-22.
  • [28] G. J. Rieger, Verallgemeinerung der Siebmethode von A. Selberg auf algebraische Zahlkörper III, J. Reine Angew. Math. 208 (1961), 79-90.
  • [29] W. Schaal, Obere und untere Abschätzungen in algebraischen Zahlkörpern mit Hilfe des linearen Selbergschen Siebes, Acta Arith. 13 (1968), 267-313.
  • [30] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, Oxford University Press, 1951.
  • [31] R. C. Vaughan, An elementary method in prime number theory, Acta Arith. 37 (1980), 111-115
Typ dokumentu
Bibliografia
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