[HTML][HTML] Real zeros of Hurwitz–Lerch zeta functions in the interval (− 1, 0)
T Nakamura - Journal of Mathematical Analysis and Applications, 2016 - Elsevier
Abstract For 0< a≤ 1, s, z∈ C and 0<| z|≤ 1, the Hurwitz–Lerch zeta function is defined by
Φ (s, a, z):=∑ n= 0∞ zn (n+ a)− s when σ:= ℜ (s)> 1. In this paper, we show that Φ (σ, a, z)≠ …
Φ (s, a, z):=∑ n= 0∞ zn (n+ a)− s when σ:= ℜ (s)> 1. In this paper, we show that Φ (σ, a, z)≠ …
Real zeros of Hurwitz–Lerch zeta and Hurwitz–Lerch type of Euler–Zagier double zeta functions
T Nakamura - … Proceedings of the Cambridge Philosophical Society, 2016 - cambridge.org
Let 0< a⩽ 1, s, z∈ and 0<| z|⩽ 1. Then the Hurwitz–Lerch zeta function is defined by Φ (s, a,
z)≔∑∞ n= 0zn (n+ a)− s when σ≔ ℜ (s)> 1. In this paper, we show that the Hurwitz zeta …
z)≔∑∞ n= 0zn (n+ a)− s when σ≔ ℜ (s)> 1. In this paper, we show that the Hurwitz zeta …
[HTML][HTML] Real zeros of Hurwitz zeta-functions and their asymptotic behavior in the interval (0, 1)
K Endo, Y Suzuki - Journal of Mathematical Analysis and Applications, 2019 - Elsevier
Abstract Let 0< a≤ 1, s∈ C, and ζ (s, a) be the Hurwitz zeta-function. Recently, Nakamura
showed that ζ (σ, a) does not vanish for any 0< σ< 1 if and only if 1/2≤ a≤ 1. In this paper …
showed that ζ (σ, a) does not vanish for any 0< σ< 1 if and only if 1/2≤ a≤ 1. In this paper …
On the behavior of multiple zeta-functions with identical arguments on the real line
K Matsumoto, T Matsusaka, I Tanackov - Journal of Number Theory, 2022 - Elsevier
We study the behavior of r-fold zeta-functions of Euler-Zagier type with identical arguments ζ
r (s, s,…, s) on the real line. Our basic tool is an “infinite” version of Newton's classical …
r (s, s,…, s) on the real line. Our basic tool is an “infinite” version of Newton's classical …
Sufficient and equivalent criteria for the Riemann Hypothesis
D Schipani - arxiv preprint arxiv:1003.2064, 2010 - arxiv.org
arxiv:1003.2064v4 [math.NT] 30 Aug 2011 Sufficient and equivalent criteria for the Riemann
Hypothesis∗ Page 1 arxiv:1003.2064v4 [math.NT] 30 Aug 2011 Sufficient and equivalent …
Hypothesis∗ Page 1 arxiv:1003.2064v4 [math.NT] 30 Aug 2011 Sufficient and equivalent …
Generalized Riemann hypotheses: sufficient and equivalent criteria
D Schipani - arxiv preprint arxiv:1005.1609, 2010 - arxiv.org
This paper presents new sufficient and equivalent conditions for the generalized version of
the Riemann Hypothesis. The paper derives also statements and remarks concerning zero …
the Riemann Hypothesis. The paper derives also statements and remarks concerning zero …
[PDF][PDF] Hurwitz zeta and Euler-Zagier-Hurwitz type of double zeta distributions and real zeros of these zeta functions
T Nakamura - arxiv preprint arxiv:1312.4712, 2013 - researchgate.net
In this paper, we give Hurwitz zeta distributions with 0< σ= 1 by using the Gamma function.
During the proof process, we show that the Hurwitz zeta function ζ (σ, a) does not vanish for …
During the proof process, we show that the Hurwitz zeta function ζ (σ, a) does not vanish for …