@article{bwmeta1.element.bwnjournal-article-aav65i1p53bwm, author = {M. D. Coleman}, title = {The Rosser-Iwaniec sieve in number fields, with an application}, journal = {Acta Arithmetica}, volume = {64}, year = {1993}, pages = {53-83}, zbl = {0784.11047}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav65i1p53bwm} }
M. D. Coleman. The Rosser-Iwaniec sieve in number fields, with an application. Acta Arithmetica, Tome 64 (1993) pp. 53-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav65i1p53bwm/
[000] [1] N. C. Ankeny, Representations of primes by quadratic forms, Amer. J. Math. 74 (1952), 913-919. | Zbl 0047.27501
[001] [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). | Zbl 0152.03501
[002] [3] M. D. Coleman, The distribution of points at which binary quadratic forms are prime, Proc. London Math. Soc. (3) 61 (1990), 433-456. | Zbl 0712.11065
[003] [4] M. D. Coleman, A zero-free region for the Hecke L-functions, Mathematika 37 (1990), 287-304. | Zbl 0721.11050
[004] [5] M. D. Coleman, The distribution of points at which norm-forms are prime, J. Number Theory 41 (1992), 359-378. | Zbl 0760.11035
[005] [6] P. X. Gallagher, A large sieve density estimate near σ = 1, Invent. Math. 11 (1970), 329-339. | Zbl 0219.10048
[006] [7] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974. | Zbl 0298.10026
[007] [8] D. R. Heath-Brown and H. Iwaniec, On the differences between consecutive primes, Invent. Math. 55 (1979), 49-69. | Zbl 0424.10028
[008] [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. | Zbl 0412.10028
[009] [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. | Zbl 46.0258.01
[010] [11] J. G. Hinz, A generalization of Bombieri's prime number theorem to algebraic number fields, Acta Arith. 51 (1988), 173-193. | Zbl 0605.10023
[011] [12] J. G. Hinz, Chen's theorem in totally real algebraic number fields, Acta Arith. 58 (1991), 335-361. | Zbl 0744.11046
[012] [13] H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202.
[013] [14] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. | Zbl 0444.10038
[014] [15] H. Iwaniec and M. Jutila, Primes in short intervals, Ark. Mat. 17 (1979), 167-176. | Zbl 0408.10029
[015] [16] D. Johnson, Mean values of Hecke L-functions, J. Reine Angew. Math. 305 (1979), 195-205. | Zbl 0392.10042
[016] [17] W. B. Jurkat and H.-E. Richert, An improvement of Selberg's sieve method, I, Acta Arith. 11 (1965), 217-240. | Zbl 0128.26902
[017] [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). | Zbl 0451.12007
[018] [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).
[019] [20] J. P. Kubilius, The decomposition of prime numbers into two squares, Dokl. Akad. Nauk SSSR (N.S.) 77 (1951), 791-794 (in Russian). | Zbl 0042.27102
[020] [21] J. P. Kubilius, On some problems of the geometry of prime numbers, Mat. Sb. (N.S.) 31 (1952), 507-542 (in Russian). | Zbl 0049.03301
[021] [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.
[022] [23] T. Mitsui, Generalised prime number theorem, Japan. J. Math. 26 (1956), 1-42. | Zbl 0126.27503
[023] [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. | Zbl 0444.12008
[024] [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.
[025] [26] S. Ricci, Local distribution of primes, Ph.D. thesis, University of Michigan, 1976.
[026] [27] H.-E. Richert, Selberg's sieve with weights, Mathematika 16 (1969), 1-22. | Zbl 0192.39703
[027] [28] G. J. Rieger, Verallgemeinerung der Siebmethode von A. Selberg auf algebraische Zahlkörper III, J. Reine Angew. Math. 208 (1961), 79-90.
[028] [29] W. Schaal, Obere und untere Abschätzungen in algebraischen Zahlkörpern mit Hilfe des linearen Selbergschen Siebes, Acta Arith. 13 (1968), 267-313. | Zbl 0155.09702
[029] [30] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, Oxford University Press, 1951. | Zbl 0042.07901
[030] [31] R. C. Vaughan, An elementary method in prime number theory, Acta Arith. 37 (1980), 111-115 | Zbl 0448.10037