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Volumn 150, Issue 1, 2011, Pages 65-91

On the least prime in an arithmetic progression and estimates for the zeros of Dirichlet L-functions

Author keywords

Dirichlet L functions; Least prime in an arithmetic progression; Linnik's constant; Linnik's theorem; Zero density estimates; Zero free regions

Indexed keywords


EID: 80051706608     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa150-1-4     Document Type: Article
Times cited : (68)

References (20)
  • 1
    • 80051723520 scopus 로고
    • On the least prime in an arithmetical progression
    • J. Chen, On the least prime in an arithmetical progression, Sci. Sinica 14 (1965), 1868-1871.
    • (1965) Sci. Sinica , vol.14 , pp. 1868-1871
    • Chen, J.1
  • 2
    • 53249104678 scopus 로고
    • On the least prime in an arithmetical progression and two theorems concerning the zeros of dirichlet's L-functions
    • J. Chen, On the least prime in an arithmetical progression and two theorems concerning the zeros of Dirichlet's L-functions, ibid. 20 (1977), 529-562.
    • (1977) Sci. Sinica. , vol.20 , pp. 529-562
    • Chen, J.1
  • 3
    • 0001315531 scopus 로고
    • On the least prime in an arithmetical progression and theorems concerning the zeros of dirichlet's L-functions II
    • -, On the least prime in an arithmetical progression and theorems concerning the zeros of Dirichlet's L-functions II, ibid. 22 (1979), 859-889.
    • (1979) Sci. Sinica. , vol.22 , pp. 859-889
    • Chen, J.1
  • 4
    • 80051774058 scopus 로고
    • On the least prime in an arithmetical progression (III), (IV)
    • 792-807
    • J. Chen and J. M. Liu, On the least prime in an arithmetical progression (III), (IV), Sci. China Ser. A 32 (1989), 654-673, 792-807.
    • (1989) Sci. China Ser. A , vol.32 , pp. 654-673
    • Chen, J.1    Liu, J.M.2
  • 5
    • 80051731012 scopus 로고
    • On the least prime in an arithmetical progression and theorems concerning the zeros of dirichlet's L-functions (V)
    • Beijing, 1988 Springer, Berlin
    • -, -, On the least prime in an arithmetical progression and theorems concerning the zeros of Dirichlet's L-functions (V), in: International Symposium in Memory of Hua Loo Keng, Vol. I (Beijing, 1988), Springer, Berlin, 1991, 19-42.
    • (1991) International Symposium in Memory of Hua Loo Keng , vol.1 , pp. 19-42
    • Chen, J.1    Liu, J.M.2
  • 7
    • 0000862833 scopus 로고
    • On linnik's constant
    • -, On Linnik's constant, Acta Arith. 39 (1981), 163-179.
    • (1981) Acta Arith. , vol.39 , pp. 163-179
    • Graham, S.W.1
  • 8
    • 84963042409 scopus 로고
    • Zero-free regions for dirichlet L-functions, and the least prime in an arithmetic progression
    • D. R. Heath-Brown, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression, Proc. London Math. Soc. (3) 64 (1992), 265-338.
    • (1992) Proc. London Math. Soc. (3) , vol.64 , pp. 265-338
    • Heath-Brown, D.R.1
  • 9
    • 12444323815 scopus 로고    scopus 로고
    • Analytic number theory
    • Amer. Math. Soc.
    • H. Iwaniec and E. Kowalski, Analytic Number Theory, Colloq. Publ. 53, Amer. Math. Soc., 2004.
    • (2004) Colloq. Publ. , vol.53
    • Iwaniec, H.1    Kowalski, E.2
  • 10
    • 80051742924 scopus 로고
    • A new estimate for linnik's constant
    • M. Jutila, A new estimate for Linnik's constant, Ann. Acad. Sci. Fenn. Ser. A I 471 (1970), 8 pp.
    • (1970) Ann. Acad. Sci. Fenn. Ser. A I , vol.471 , pp. 8
    • Jutila, M.1
  • 11
    • 0002723939 scopus 로고
    • On linnik's constant
    • -, On Linnik's constant, Math. Scand. 41 (1977), 45-62.
    • (1977) Math. Scand. , vol.41 , pp. 45-62
    • Jutila, M.1
  • 12
    • 0000985116 scopus 로고
    • On the least prime in an arithmetic progression I. The basic theorem
    • Yu. 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.
    • (1944) Rec. Math. (Mat. Sbornik) N.S. , vol.15 , Issue.57 , pp. 139-178
    • Linnik, Yu.V.1
  • 13
    • 0012910692 scopus 로고
    • On the least prime in an arithmetic progression II. The deuring-heilbronn phenomenon
    • -, On the least prime in an arithmetic progression II. The Deuring-Heilbronn phenomenon, Rec. Math. (Mat. Sbornik) N.S. 15 (57) (1944), 347-368.
    • (1944) Rec. Math. (Mat. Sbornik) N.S. , vol.15 , Issue.57 , pp. 347-368
    • Linnik, Yu.V.1
  • 14
    • 0032430049 scopus 로고    scopus 로고
    • A numerical bound for small prime solutions of some ternary linear equations
    • M. C. Liu and T. Wang, A numerical bound for small prime solutions of some ternary linear equations, Acta Arith. 86 (1998), 343-383. (Pubitemid 128335680)
    • (1998) Acta Arithmetica , vol.86 , Issue.4 , pp. 343-383
    • Liu, M.-C.1    Wang, T.2
  • 15
    • 27544469009 scopus 로고
    • On the least prime in an arithmetical progression
    • C. D. Pan, On the least prime in an arithmetical progression, Sci. Record (N.S.) 1 (1957), 311-313.
    • (1957) Sci. Record (N.S.) , vol.1 , pp. 311-313
    • Pan, C.D.1
  • 16
    • 80051750513 scopus 로고
    • On the least prime in an arithmetical progression
    • -, On the least prime in an arithmetical progression, Acta Sci. Natur. Univ. Pekinensis 4 (1958), 1-34.
    • (1958) Acta Sci. Natur. Univ. Pekinensis , vol.4 , pp. 1-34
    • Pan, C.D.1
  • 17
    • 80051742556 scopus 로고
    • On some recent results in the analytic theory of numbers
    • Amer. Math. Soc., Providence, RI
    • P. Turán, On some recent results in the analytic theory of numbers, in: Number Theory Institute, 1969, Proc. Sympos. Pure Math. 20, Amer. Math. Soc., Providence, RI, 1971, 359-374.
    • (1971) Number Theory Institute, 1969, Proc. Sympos. Pure Math. , vol.20 , pp. 359-374
    • Turán, P.1
  • 18
    • 80051727473 scopus 로고
    • On the least prime in an arithmetic progression
    • W. Wang, On the least prime in an arithmetic progression, Acta Math. Sinica 29 (1986), 826-836.
    • (1986) Acta Math. Sinica , vol.29 , pp. 826-836
    • Wang, W.1
  • 19
    • 51249171106 scopus 로고
    • On the least prime in an arithmetic progression
    • -, On the least prime in an arithmetic progression, ibid. 7 (1991), 279-289.
    • (1991) Acta Math. Sinica. , vol.7 , pp. 279-289
    • Wang, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.