In a recent investigation of dihedral quartic fields  a rational sequcnce (an) was encountered. We show that these a„ arc positive integers and that thcy satisfy surprising congruences modulo a prime p. Thcy generate unknown p-adic numbers and may therefore be comparcd with the cubic recurrences in , where the corresponding p-adic numbers are known completely . Other unsolved problems are presented. Thc growth of thc a„ is examined and a new algorithm for computing a„ is givcn. An appcndix by D. Zagier, which carries thc investigation furthcr, is added.
Modular Form Eisenstein Series Modular Function Congruence Subgroup General Congruence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access