Math @ Duke

Publications [#9242] of Joshua B. Holden
Papers Published
 Joshua Holden, Irregularity of prime numbers over real quadratic fields,
In: Algorithmic number theory: third international symposium;proceedings, no. 1423 in Springer Lecture Notes in Computer Science, SpringerVerlag, 1998
[MR2000m:11113], [available here]
(last updated on 2000/12/22)
Abstract: The concept of regular and irregular primes has played an
important
role in number theory at least since the time of Kummer. We
extend
this concept to the setting of arbitrary totally real number
fields $k_{0}$,
using the values of the zeta function $\zeta_{k_{0}}$ at
negative
integers as our ``higher Bernoulli numbers''. Once we have
defined
$k_{0}$regular primes and the index of
$k_{0}$irregularity, we
discuss how to compute these indices when $k_{0}$ is a real
quadratic
field. Finally, we present the results of some preliminary
computations, and show that the frequency of various indices
seems to
agree with those predicted by a heuristic argument.


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