A new application of the gram points
Sign Up to like & getrecommendations! Published in 2019 at "Aequationes mathematicae"
DOI: 10.1007/s00010-019-00647-8
Abstract: The Gram points $$t_n$$tn are defined as solutions of the equation $$\theta (t)=(n-1)\pi $$θ(t)=(n-1)π, $$n\in \mathbb {N}$$n∈N, where $$\theta (t)$$θ(t), $$t>0$$t>0, denotes the increment of the argument of the function $$\pi ^{-s/2}\Gamma \left( \frac{s}{2}\right) $$π-s/2Γs2… read more here.
Keywords: application gram; gram; gram points; new application ... See more keywords
Gram points in the theory of zeta-functions of certain cusp forms
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125396
Abstract: Abstract In the paper, an analogue of the Gram points used in the theory of the Riemann zeta-function is introduced for zeta-functions of normalized Hecke-eigen cusp forms of weight κ. Some analytic properties of those… read more here.
Keywords: points theory; functions certain; zeta functions; cusp forms ... See more keywords
A new discriminant for the Z-function and a Dyson-like repulsion for consecutive zeros
Sign Up to like & getrecommendations! Published in 2025 at "Physica Scripta"
DOI: 10.1088/1402-4896/adf3f1
Abstract: Let Z(t)=ζ12+ite−iθ(t) be the Hardy Z-function, where ζ(σ + it) is the Riemann zeta function and θ(t) is the Riemann-Siegel θ-function. In 1903 Gram introduced Gram’s law (−1)nZ(gn)>0, where gn is the unique solution of… read more here.
Keywords: function; dyson; new discriminant; discriminant function ... See more keywords
Joint Discrete Approximation of Analytic Functions by Shifts of the Riemann Zeta-Function Twisted by Gram Points
Sign Up to like & getrecommendations! Published in 2023 at "Mathematics"
DOI: 10.3390/math11030565
Abstract: Let θ(t) denote the increment of the argument of the product π−s/2Γ(s/2) along the segment connecting the points s=1/2 and s=1/2+it, and tn denote the solution of the equation θ(t)=(n−1)π, n=0,1,⋯. The numbers tn are… read more here.
Keywords: functions shifts; gram points; riemann zeta; analytic functions ... See more keywords