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• W2101471654 abstract "We present an improved algorithm for tabulating class groups of imaginary quadratic fields of bounded discriminant. Our method uses classical class number formulas involving theta-series to compute the group orders unconditionally for all $Delta not equiv 1 pmod{8}.$ The group structure is resolved using the factorization of the group order. The $1 bmod 8$ case was handled using the methods of cite{jacobson}, including the batch verification method based on the Eichler-Selberg trace formula to remove dependence on the Extended Riemann Hypothesis. Our new method enabled us to extend the previous bound of $|Delta| < 2 cdot 10^{11}$ to $2^{40}$. Statistical data in support of a variety conjectures is presented, along with new examples of class groups with exotic structures." @default.
• W2101471654 created "2016-06-24" @default.
• W2101471654 creator A5017460809 @default.
• W2101471654 creator A5019170629 @default.
• W2101471654 date "2015-11-03" @default.
• W2101471654 modified "2023-09-23" @default.
• W2101471654 title "Unconditional class group tabulation of imaginary quadratic fields to $|Delta | < 2^{40}$" @default.
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• W2101471654 doi "https://doi.org/10.1090/mcom3050" @default.
• W2101471654 hasPublicationYear "2015" @default.
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