Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (3): 1179-1188.doi: 10.1016/S0252-9602(11)60308-1

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ON THE EXCEPTIONAL FIELDS FOR A CLASS OF REAL QUADRATIC FIELDS

 LIU Li1,2, LIU Hong-Wen2   

  1. 1. School of Mathematics, Hefei University of Technology, Hefei 230009, China
    2. Department of Mathematics, Tongji University, Shanghai 200092, China
  • Received:2008-04-13 Revised:2010-02-05 Online:2011-05-20 Published:2011-05-20
  • Supported by:

    Project supported by the NSFC (10801105; 30871444), the Key Project of Natural Science of Anhui Provincial Department of Education (KJ2009A44), the Doctoral Special Fund of Hefei University of Technology (GDBJ2010-012) and the Key Project of Science and Technology of Anhui Province (08010302070).

Abstract:

In this paper, we give a lower bound exp(2.2×108) for those discriminants of real quadratic fields Q(√d) with d = N2 − 4 and h(d) = 1.

Key words: quadratic field, class number, discriminant, Zeta-function, lower bound

CLC Number: 

  • 11R11
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