Algorithmic Number Theory

Volume 1423 of the series Lecture Notes in Computer Science pp 412-423


Timing analysis of targeted hunter searches

  • John W. JonesAffiliated withDepartment of Mathematics, Arizona State University
  • , David P. RobertsAffiliated withDepartment of Mathematics, Hill Center, Rutgers University

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One can determine all primitive number fields of a given degree and discriminant with a finite search of potential defining polynomials. We develop an asymptotic formula for the number of polynomials which need to be inspected which reflects both archimedean and non-archimedean restrictions placed on the coefficients of a defining polynomial.