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Original Articles

An Investigation of Bounds for the Regulator of Quadratic Fields

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Pages 211-225 | Published online: 03 Apr 2012

REFERENCES

  • Bach , E. 1994 . “Improved approximations for Euler products” [Bach 1994], unpublished manuscript
  • Chowla , S. 1949 . “Improvement of a theorem of Linnik and Walfisz” . Proc. London Math. Soc. , 50 : 423 – 429 . [Chowla 1949]
  • Cohen , H. , Diaz y Diaz , F. and Olivier , M. 1993 . “Calculs de nombres de classes et de régulateurs de corps quadratiques en temps sousexponentiel”. ” . In Séminaire de Théorie des Nombres de Paris 1990–1991 35 – 46 . Boston : Birkhäuser. . [Cohen et al. 1993], Progress in Math. 108
  • Cohen , H. and Lenstra , H. W. Jr. 1983 . “Heuristics on class groups”. ” . In Number Theory, CUNY, 1982 Edited by: Chudnovsky , D. V. 26 – 36 . New York : Springer. . [Cohen and Lenstra 1983], Lecture Notes in Math. 1052
  • Cohen , H. and Lenstra , H. W. Jr. 1984 . “Heuristics on class groups of number fields”. ” . In Number Theory, Noordwijkerhout, 1983 Edited by: Jager , H. 33 – 62 . New York : Springer. . [Cohen and Lenstra 1984], Lecture Notes in Math. 1068
  • Elliot , P. D. T. A. 1969 . “On the size of L(1,χ)” . J. reine angew. Math. , 236 : 26 – 36 . [Elliot 1969]
  • Halter-Koch , F. 1989 . “Reell-quadratischer Zahlkörper mit größer Grundeinheit” . Abh. Math. Sem. Univ. Hamburg , 59 : 171 – 181 . [Halter-Koch 1989]
  • Hooley , C. 1984 . “On the Pellian equation and the class number of indefinite binary quadratic forms” . J. reine angew. Math. , 353 : 98 – 131 . [Hooley 1984]
  • Hua , L. K. 1982 . Introduction to Number Theory New York : Springer. . [Hua 1982]
  • Joshi , P. T. 1970 . “The size of L(1,χ) for real nonprincipal residue characters χ with prime modulus” . J. Number Theory , 2 : 58 – 73 . [Joshi 1970]
  • Landau , E. 1936 . “On a Titchmarsh–Estermann sum” . J. London Math. Soc. , 11 : 242 – 245 . [Landau 1936]
  • Lehmer , D. H. , Lehmer , E. and Shanks , D. 1970 . “Integer sequences having prescribed quadratic character” . Math. Comp. , 24 : 433 – 451 . [Lehmer et al. 1970]
  • Lenstra , H. W. Jr. 1982 . “On the Calculation of Regulators and Class Numbers of Quadratic Fields”. ” . In Number Theory Days 123 – 150 . Cambridge : Cambridge U. Press. . [Lenstra 1982], Exeter, 1980, London Math. Soc. Lecture Note Series 56
  • Littlewood , J. E. 1928 . “On the class number of the corpus P(√−k)” . Proc. London Math. Soc. , 27 : 358 – 372 . [Littlewood 1928]
  • Lukes , R. F. , Patterson , C. D. and Williams , H. C. 1995 . “Numerical Sieving Devices: Their History and Some Applications” . Nieuw Archief voor Wiskunde (4) , 13 : 113 – 139 . [Lukes et al. 1995]
  • Lukes , R. F. , Patterson , C. D. and Williams , H. C. “Some results on pseudosquares” [Lukes et al. a], to appear in Math. Comp.
  • Mollin , R. A. and Williams , H. C. 1992 . “Computation of the class number of a real quadratic field” . Utilitas Math. , 41 : 259 – 308 . [Mollin and Williams]
  • Nagell , T. 1922 . “Zur Arithmetik der Polynome” . Abh. Math. Sem. Univ. Hamburg , 1 : 179 – 194 . [Nagell 1922]
  • Oesterlé , J. 1978 . “Versions effectives du théorème de Chebotarev sous l'hypothése de Riemann généralisée”. ” . In Journées arithmétiques 165 – 167 . Luminy. . [Oesterlé 1979], Astérisque 61, Soc. Math. de France, Paris, 1979
  • Shanks , D. 1969 . “Class number, a theory of factorization and genera”. ” . In Number Theory Institute 415 – 440 . Stony Brook. . [Shanks 1971], Proc. Symp. Pure Math. 20, Amer. Math. Soc., Providence, 1971
  • Shanks , D. 1973 . “Systematic examination of Littlewood's bounds on L(1,χ)”. ” . In Analytic number theory, St. Louis, 1972 Edited by: Diamond , H. G. 267 – 283 . Providence : Amer. Math. Soc. . [Shanks 1973], Proc. Symp. Pure Math. 24
  • Stephens , A. J. and Williams , H. C. 1988 . “Computation of real quadratic fields with class number one” . Math. Comp. , 51 : 809 – 824 . [Stephens and Williams 1988]

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