Publications [#9242] of Joshua B. Holden

Papers Published

1. 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, Springer-Verlag, 1998
   (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.