论文标题
高斯周期是完全真实的质量循环场的最小多项式
Gauss periods are minimal polynomials for totally real cyclic fields of prime degree
论文作者
论文摘要
我们报告了广泛的计算证据，表明高斯周期方程是代表Prime度$ P $的Abelian（环状）多项式的原始元素的最小判别多项式。通过计算最高$ p = 97 $的200个周期方程，我们在Klüners和Malle的Compendiuits Number字段数据库中大大扩展了表。最多$ p = 7 $，周期方程将已知结果复制被证明具有最低歧视性。以$ 11 \ leq p \ leq 23 $，周期方程与数据库中的53个已知但未经证实的最小判别案例一致，并填补了19例缺失案例的空白。以$ 29 \ LEQ P \ LEQ 97 $，我们报告了128个以前未知的案例，其中16个猜想是Galois Group $ pt1 $的最低判别多项式。周期方程的显着优势在于，它们都可以使用适用于任意程度的领域的过程进行分析获得，并且通过系统的数值搜索很难检测到它们。
We report extensive computational evidence that Gauss period equations are minimal discriminant polynomials for primitive elements representing Abelian (cyclic) polynomials of prime degrees $p$. By computing 200 period equations up to $p=97$, we significantly extend tables in the compendious number fields database of Klüners and Malle. Up to $p=7$, period equations reproduce known results proved to have minimum discriminant. For $11\leq p\leq 23$, period equations coincide with 53 known but unproved cases of minimum discriminant in the database, and fill a gap of 19 missing cases. For $29\leq p\leq 97$, we report 128 not previously known cases, 16 of them conjectured to be minimum discriminant polynomials of Galois group $pT1$. The significant advantage of period equations is that they all may be obtained analytically using a procedure that works for fields of arbitrary degrees, and which are extremely hard to detect by systematic numerical search.
