Results 31 to 40 of about 72,493 (237)
Some Numerical Significance of the Riemann Zeta Function
Recent Advances in Natural Sciences, 2023 In this paper, the Riemann analytic continuation formula (RACF) is derived from Euler’s quadratic equation. A nonlinear function and a polynomial function that were required in the derivation were also obtained.
Opeyemi O. Enoch, Lukman O. Salaudeen
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General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function
Математичні Студії, 2021 The purpose of this paper is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
R. Frontczak, T. Goy
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Questions around the nontrivial zeros of the Riemann zeta-function. Computations and classifications
Mathematical Modelling and Analysis, 2011 We study the sequence of nontrivial zeros of the Riemann zeta-function with respect to sequences of zeros of other related functions, namely, the Hurwitz zeta-function and the derivative of Riemann's zeta-function.
Ramūnas Garunkštis, Joern Steuding
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Hamiltonian for the Zeros of the Riemann Zeta Function. [PDF]
Physical Review Letters, 2016 A Hamiltonian operator H[over ^] is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function.
C. Bender, D. Brody, Markus P. Müller
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Quantization of the Riemann Zeta-Function and Cosmology [PDF]
, 2007 Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories.
Barnaby N. +18 more
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Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line [PDF]
Communications on Pure and Applied Mathematics, 2016 We prove the leading order of a conjecture by Fyodorov, Hiary, and Keating about the maximum of the Riemann zeta function on random intervals along the critical line.
L. Arguin +4 more
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Supersymmetry and the Riemann zeros on the critical line
Physics Letters B, 2019 We propose a new way of studying the Riemann zeros on the critical line using ideas from supersymmetry. Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the strip ...
Ashok Das, Pushpa Kalauni
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The number of Goldbach representations of an integer [PDF]
, 2010 We prove the following result: Let $N \geq 2$ and assume the Riemann Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2 \sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log^{3}N), \] where $\rho=1/2+i\gamma$ runs over the non ...
Languasco, Alessandro +1 more
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Some identities related to Riemann zeta-function
Journal of Inequalities and Applications, 2016 It is well known that the Riemann zeta-function ζ ( s ) $\zeta(s)$ plays a very important role in the study of analytic number theory. In this paper, we use the elementary method and some new inequalities to study the computational problem of one kind of
Lin Xin
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Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines [PDF]
Computational methods in Function Theory, 2020 For an arbitrary complex number $$a\ne 0$$ a ≠ 0 we consider the distribution of values of the Riemann zeta-function $$\zeta $$ ζ at the a -points of the function $$\Delta $$ Δ which appears in the functional equation $$\zeta (s)=\Delta (s)\zeta (1-s ...
J. Steuding, Ade Irma Suriajaya
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