论文标题
不确定Zeta功能的Kronecker极限公式
A Kronecker limit formula for indefinite zeta functions
论文作者
论文摘要
我们证明了Kronecker的第二个极限公式的类似物，用于连续的“无限Zeta函数”。 Zwegers定义的无限theta函数的梅林变换，在作者的先前论文中引入了无限的Zeta函数。我们的公式在s = 1或s = 0时在尺寸g = 2中有效。为了选择遵守某个对称性的参数，不确定的zeta函数是一个实际二次场的射线类别Zeta Zeta Zeta Zeta函数，其特殊值在$ s = 0 $中被Stark猜想是代数单位的对数。我们的公式还允许对Stark Ray类不变的实用高精度计算。
We prove an analogue of Kronecker's second limit formula for a continuous family of "indefinite zeta functions". Indefinite zeta functions were introduced in the author's previous paper as Mellin transforms of indefinite theta functions, as defined by Zwegers. Our formula is valid in dimension g=2 at s=1 or s=0. For a choice of parameters obeying a certain symmetry, an indefinite zeta function is a differenced ray class zeta function of a real quadratic field, and its special value at $s=0$ was conjectured by Stark to be a logarithm of an algebraic unit. Our formula also permits practical high-precision computation of Stark ray class invariants.
