• Title/Summary/Keyword: Riemann hypothesis

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A NOTE ON KADIRI'S EXPLICIT ZERO FREE REGION FOR RIEMANN ZETA FUNCTION

  • Jang, Woo-Jin;Kwon, Soun-Hi
    • Journal of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1291-1304
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    • 2014
  • In 2005 Kadiri proved that the Riemann zeta function ${\zeta}(s)$ does not vanish in the region $$Re(s){\geq}1-\frac{1}{R_0\;{\log}\;{\mid}Im(s){\mid}},\;{\mid}Im(s){\mid}{\geq}2$$ with $R_0=5.69693$. In this paper we will show that $R_0$ can be taken $R_0=5.68371$ using Kadiri's method together with Platt's numerical verification of Riemann Hypothesis.

Convergence and the Riemann hypothesis

  • Lee, Jung-Seob
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.57-62
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    • 1996
  • For $1 < p \leq 2$ it is shown that a certain sequence of functions converges to -1 in $L^{p-\varepsilon}(0, 1)$ for any small $\varepsilon > 0$ if and only if the Riemann zeta function satisfies $\zeta(s) \neq 0$ for $\sigma = Re s > 1/p$.

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A NOTE ON THE ZEROS OF JENSEN POLYNOMIALS

  • Kim, Young-One;Lee, Jungseob
    • Journal of the Korean Mathematical Society
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    • v.59 no.4
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    • pp.775-787
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    • 2022
  • Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some recent results on Jensen polynomials, relevant to the Riemann hypothesis, are extended and improved.

Numerical Analysis of Nonlinear Combustion Instability Using Pressure-Sensitive Time Lag Hypothesis (시간지연 모델을 이용한 비선형 연소불안정 해석기법 연구)

  • Park Tae-Seon;Kim Seong-Ku
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.30 no.7 s.250
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    • pp.671-681
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    • 2006
  • This study focuses on the development of numerical procedure to analyze the nonlinear combustion instabilities in liquid rocket engine. Nonlinear behaviors of acoustic instabilities are characterized by the existence of limit cycle in linearly unstable engines and nonlinear or triggering instability in linearly stable engines. To discretize convective fluxes with high accuracy and robustness, approximated Riemann solver based on characteristics and Euler-characteristic boundary conditions are employed. The present procedure predicts well the transition processes from initial harmonic pressure disturbance to N-like steep-fronted shock wave in a resonant pipe. Longitudinal pressure oscillations within the SSME(Space Shuttle Main Engine) engine have been analyzed using the pressure-sensitive time lag model to account for unsteady combustion response. It is observed that the pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions.

MEAN VALUES OF DERIVATIVES OF L-FUNCTIONS IN FUNCTION FIELDS: IV

  • Andrade, Julio;Jung, Hwanyup
    • Journal of the Korean Mathematical Society
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    • v.58 no.6
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    • pp.1529-1547
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    • 2021
  • In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.

ANALYTIC SOLUTION OF HIGH ORDER FRACTIONAL BOUNDARY VALUE PROBLEMS

  • Muner M. Abou Hasan;Soliman A. Alkhatib
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.3
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    • pp.601-612
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    • 2023
  • The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

Numerical Analysis of Nonlinear Longitudinal Combustion Instability in LRE Using Pressure-Sensitive Time-Lag Hypothesis (시간지연 모델을 이용한 액체로켓엔진의 축방향 비선형 연소불안정 해석)

  • Kim Seong-Ku;Choi Hwan Seok;Park Tae Seon;Kim Yong-Mo
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • v.y2005m4
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    • pp.281-287
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    • 2005
  • Nonlinear behaviors such as steep-fronted wave motions and a finite amplitude limit cycle often accompanying combustion instabilities have been numerically investigated using a characteristic-based approximate Riemann solver and the well-known ${\eta}-{\tau}$ model. A resonant pipe initially subjected to a harmonic pressure disturbance described the natural steepening process that leads to a shocked N-wave. For a linearly unstable regime, pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions. For the 1.5 MW gas generator under development in KARI, the numerical results show good agreement with experimental data from hot-firing tests.

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