论文标题
在二次数字字段中，半融合重量的尖端形式的傅立叶系数的符号变化
Sign changes of Fourier coefficients of cusp forms of half-integral weight over split and inert primes in quadratic number fields
论文作者
论文摘要
在本文中，我们研究了半融合体重尖的傅立叶系数的符号变化。在固定的Square类$ t \ Mathbb {z}^2 $中，我们调查了$ tp^2 $ th系数中的符号变化，因为$ p $通过split或intert primes在整数上的折扣上运行，以二次延伸。我们表明，当存在一个质量时，在两组素数中都会发生符号变化，该素数分开了该场的判别，而该域的歧视性不会划分尖端形式的水平，并找到一个明确的条件，该条件确定符号变化是否发生时是否会发生符号变化。
In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class $t\mathbb{Z}^2$, we investigate the sign changes in the $tp^2$-th coefficient as $p$ runs through the split or inert primes over the ring of integers in a quadratic extension of the rationals. We show that sign changes occur in both sets of primes when there exists a prime dividing the discriminant of the field which does not divide the level of the cusp form and find an explicit condition that determines whether sign changes occur when every prime dividing the discriminant also divides the level.
