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

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1. [1] N. C. Ankeny, Representations of primes by quadratic forms, Amer. J. Math. 74 (1952), 913-919. Zbl0047.27501
2. [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). Zbl0152.03501
3. [3] M. D. Coleman, The distribution of points at which binary quadratic forms are prime, Proc. London Math. Soc. (3) 61 (1990), 433-456. Zbl0712.11065
4. [4] M. D. Coleman, A zero-free region for the Hecke L-functions, Mathematika 37 (1990), 287-304. Zbl0721.11050
5. [5] M. D. Coleman, The distribution of points at which norm-forms are prime, J. Number Theory 41 (1992), 359-378. Zbl0760.11035
6. [6] P. X. Gallagher, A large sieve density estimate near σ = 1, Invent. Math. 11 (1970), 329-339. Zbl0219.10048
7. [7] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
8. [8] D. R. Heath-Brown and H. Iwaniec, On the differences between consecutive primes, Invent. Math. 55 (1979), 49-69. Zbl0424.10028
9. [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. Zbl0412.10028
10. [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. Zbl46.0258.01
11. [11] J. G. Hinz, A generalization of Bombieri's prime number theorem to algebraic number fields, Acta Arith. 51 (1988), 173-193. Zbl0605.10023
12. [12] J. G. Hinz, Chen's theorem in totally real algebraic number fields, Acta Arith. 58 (1991), 335-361. Zbl0744.11046
13. [13] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202. 
14. [14] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. Zbl0444.10038
15. [15] H. Iwaniec and M. Jutila, Primes in short intervals, Ark. Mat. 17 (1979), 167-176. Zbl0408.10029
16. [16] D. Johnson, Mean values of Hecke L-functions, J. Reine Angew. Math. 305 (1979), 195-205. Zbl0392.10042
17. [17] W. B. Jurkat and H.-E. Richert, An improvement of Selberg's sieve method, I, Acta Arith. 11 (1965), 217-240. Zbl0128.26902
18. [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). Zbl0451.12007
19. [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. [20] J. P. Kubilius, The decomposition of prime numbers into two squares, Dokl. Akad. Nauk SSSR (N.S.) 77 (1951), 791-794 (in Russian). Zbl0042.27102
21. [21] J. P. Kubilius, On some problems of the geometry of prime numbers, Mat. Sb. (N.S.) 31 (1952), 507-542 (in Russian). Zbl0049.03301
22. [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. [23] T. Mitsui, Generalised prime number theorem, Japan. J. Math. 26 (1956), 1-42. Zbl0126.27503
24. [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. Zbl0444.12008
25. [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. [26] S. Ricci, Local distribution of primes, Ph.D. thesis, University of Michigan, 1976. 
27. [27] H.-E. Richert, Selberg's sieve with weights, Mathematika 16 (1969), 1-22. Zbl0192.39703
28. [28] G. J. Rieger, Verallgemeinerung der Siebmethode von A. Selberg auf algebraische Zahlkörper III, J. Reine Angew. Math. 208 (1961), 79-90. 
29. [29] W. Schaal, Obere und untere Abschätzungen in algebraischen Zahlkörpern mit Hilfe des linearen Selbergschen Siebes, Acta Arith. 13 (1968), 267-313. Zbl0155.09702
30. [30] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, Oxford University Press, 1951. Zbl0042.07901
31. [31] R. C. Vaughan, An elementary method in prime number theory, Acta Arith. 37 (1980), 111-115 Zbl0448.10037

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