Exceptional characters and prime numbers in arithmetic progressions

International Mathematics Research Notices

Volumn , Issue 37, 2003, Pages 2033-2050

  Friedlander, John B ^a   Iwaniec, Henryk ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042835581     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792803130784     Document Type: Article

References (16)

1. J. B. Conrey and H. Iwaniec, Spacing of zeros of Hecke L-functions and the class number problem, Acta Arith. 103 (2002), no. 3, 259-312.
2. M. Deuring, Imaginäre quadratische Zahlkörper mit der Klassenzahl I, Math. Z. 37 (1933), 405-415 (German).
3. P. G. L. Dirichlet, Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält, Abh. Kön Preuss. Akad. der Wissens 34 (1837), 45-81 (German), reprinted in Collected Works, Chelsea, New York, 1969, pp. 313-342.
4. J. B. Friedlander, On the class numbers of certain quadratic extensions, Acta Arith. 28 (1976), no. 4, 391-393.
5. J. B. Friedlander and H. Iwaniec, Incomplete Kloosterman sums and a divisor problem. With an appendix by B. J. Birch and E. Bombieri, Ann. of Math. (2) 121 (1985), no. 2, 319-350.
6. -, Asymptotic sieve for primes, Ann. of Math. (2) 148 (1998), no. 3, 1041-1065.
7. D. M. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 4, 624-663.
8. D. R. Heath-Brown, Prime twins and Siegel zeros, Proc. London Math. Soc. (3) 47 (1983), no. 2, 193-224.
9. -, Siegel zeros and the least prime in an arithmetic progression, Quart. J. Math. Oxford Ser. (2) 41 (1990), no. 164, 405-418.
10. -, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression, Proc. London Math. Soc. (3) 64 (1992), no. 2, 265-338.
11. H. Heilbronn, On the class-number in imaginary quadratic fields, Quart. J. Math. Oxford Ser. 5 (1934), 150-160.
12. E. Landau, Über die Klassenzahl imaginär-quadratischer Zahlkörper, Gött. Nachr. (1918), 285- 295 (German).
13. -, Bemerkungen zum Heilbronnschen Satz, Acta Arith. 1 (1935), 1-18 (German).
14. U. V. Linnik, On the least prime in an arithmetic progression. I. The basic theorem, Rec. Math. [Mat. Sbornik] N.S. 15(57) (1944), 139-178.
15. -, On the least prime in an arithmetic progression. II. The Deuring-Heilbronn phenomenon, Rec. Math. [Mat. Sbornik] N.S. 15(57) (1944), 347-368.
16. C. L. Siegel, Über die Classenzahl quadratischer Zahlkörper, Acta Arith. 1 (1935), 83-86 (German).