Hecke operators and the weight distributions of certain codes
Journal of Combinatorial Theory Series A
A course in computational algebraic number theory
A course in computational algebraic number theory
On some computational problems in finite Abelian groups
Mathematics of Computation
Applying sieving to the computation of quadratic class groups
Mathematics of Computation
Experimental Results on Class Groups of Real Quadratic Fields
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Numerical results on class groups of imaginary quadratic fields
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Numerical results on class groups of imaginary quadratic fields
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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Using techniques described in [3], we have computed the class number and class group structure of all imaginary quadratic fields with discriminant Δ for 0 11. A novel verification algorithm based on the Eichler Selberg Trace Formula [15] was used to ensure that the correctness of our results does not rely on any unproved hypothesis. We present the results of our computations, and remark on specific evidence that was found pertaining to a number of heuristics. In particular, we present data which supports some of the Cohen-Lenstra heuristics [8], Littlewood’s bounds on L(1,χ) [14], and Bach’s bound on the maximum norm of the prime ideals required to generate the class group [1].