Functional equation and zeros on the critical line of the quadrilateral zeta function.
Functional equation and zeros on the critical line of the quadrilateral zeta function.
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函数方程和四边形 zeta 函数临界线上的零点。
DOI：
10.1016/j.jnt.2021.06.017
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Takashi Nakamura
中科院分区：
文献类型：
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作者：
Takashi Nakamura;Takashi Nakamura
对于0<；a≤1/2，我们利用Hurwitz函数和周期Zeta函数定义了四边形Zeta函数Q(S，a)，并证明了Q(S，a)满足Hamburger，Heck和Knopp研究的Riemann函数方程.此外，我们证明了对于任意的0&a≤1/2，存在正常数A(A)和T0(A)，使得当T≥T0(A)时，四边形Zeta函数Q(S，a)在从1/2到1/2+ITT的直线段上的零点个数大于A(A)T。
Abstract For 0< a≤ 1/2, we define the quadrilateral zeta function Q (s, a) using the Hurwitz and periodic zeta functions and show that Q (s, a) satisfies Riemann's functional equation studied by Hamburger, Heck and Knopp. Moreover, we prove that for any 0< a≤ 1/2, there exist positive constants A (a) and T 0 (a) such that the number of zeros of the quadrilateral zeta function Q (s, a) on the line segment from 1/2 to 1/2+ i T is greater than A (a) T whenever T≥ T 0 (a).