On a solution to a functional equation
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Alexander E. Patkowski
Abstract
We offer a solution to a functional equation using properties of the Mellin transform. A new criteria for the Riemann Hypothesis is offered as an application of our main result, through a functional relationship with the Riemann xi function.
References
[1] H. M. Edwards, Riemann’s Zeta Function, Dover, Mineola, 1974. Suche in Google Scholar
[2] H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ. 53, American Mathematical Society, Providence, 2004. 10.1090/coll/053Suche in Google Scholar
[3] R. B. Paris and D. Kaminski, Asymptotics and Mellin–Barnes Integrals, Cambridge University, Cambridge, 2001. 10.1017/CBO9780511546662Suche in Google Scholar
[4] E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd ed., Oxford University, Oxford, 1986. Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- L 1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative
- On tangential approximations of the solution set of set-valued inclusions
- Stabilization of the wave equation with a nonlinear delay term in the boundary conditions
- Fixed point to fixed circle and activation function in partial metric space
- A note on the validity of the Schrödinger approximation for the Helmholtz equation
- Certain classes of analytic functions defined by Hurwitz–Lerch zeta function
- A new factor theorem on absolute matrix summability method
- On a solution to a functional equation
- Hydromagnetic effects on non-Newtonian Hiemenz flow
- Stability of a class of entropies based on fractional calculus
- Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion
- Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts
- Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control
- On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions
- Extended homogeneous balance conditions in the sub-equation method
Artikel in diesem Heft
- Frontmatter
- L 1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative
- On tangential approximations of the solution set of set-valued inclusions
- Stabilization of the wave equation with a nonlinear delay term in the boundary conditions
- Fixed point to fixed circle and activation function in partial metric space
- A note on the validity of the Schrödinger approximation for the Helmholtz equation
- Certain classes of analytic functions defined by Hurwitz–Lerch zeta function
- A new factor theorem on absolute matrix summability method
- On a solution to a functional equation
- Hydromagnetic effects on non-Newtonian Hiemenz flow
- Stability of a class of entropies based on fractional calculus
- Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion
- Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts
- Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control
- On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions
- Extended homogeneous balance conditions in the sub-equation method
