论文标题
新形式的根号偏差
Root number bias for newforms
论文作者
论文摘要
以前，我们观察到，新形式对根号$+1 $ squarefreame级别遵守：$ s_k（γ_0（n））$中至少有一半的新形式，而根号$+1 $ for $ n $ squarefree，并且在少数特殊情况下，它的一半以上是一半以上。随后，其他作者处理的水平是无方数字的立方体。在这里，我们对待任意水平，发现如果水平不是无方数的平方，那么这种严格的偏见仍然具有任何重量。实际上，这种特殊级别的数量是固定重量有限的，如果$ k <12 $，则为0。我们还研究了这个问题的一些变体，以更好地理解出色的水平。
Previously we observed that newforms obey a strict bias towards root number $+1$ in squarefree levels: at least half of the newforms in $S_k(Γ_0(N))$ with root number $+1$ for $N$ squarefree, and it is strictly more than half outside of a few special cases. Subsequently, other authors treated levels which are cubes of squarefree numbers. Here we treat arbitrary levels, and find that if the level is not the square of a squarefree number, this strict bias still holds for any weight. In fact the number of such exceptional levels is finite for fixed weight, and 0 if $k < 12$. We also investigate some variants of this question to better understand the exceptional levels.
