تقرير
Unconditional Class Group Tabulation of Imaginary Quadratic Fields to $|\Delta| < 2^{40}$
| العنوان: | Unconditional Class Group Tabulation of Imaginary Quadratic Fields to $|\Delta| < 2^{40}$ |
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| المؤلفون: | Mosunov, A. S., Jacobson Jr, M. J. |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | 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. Comment: 26 pages, 2 figures, to appear in Math. Comp |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1502.07953 |
| رقم الأكسشن: | edsarx.1502.07953 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |