Displaying similar documents to “On some problems involving Hardy’s function”

On the riemann zeta-function and the divisor problem

Aleksandar Ivić (2004)

Open Mathematics

Similarity:

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of ς 1 2 + i t . If E * t = E t - 2 π Δ * t / 2 π with Δ * x = - Δ x + 2 Δ 2 x - 1 2 Δ 4 x , then we obtain ∫ 0 T E * t 4 d t ≪ e T 16 / 9 + ε . We also show how our method of proof yields the bound ∑ r = 1 R ∫ t r - G t r + G ς 1 2 + i t 2 d t 4 ≪ e T 2 + e G - 2 + R G 4 T ε , where T 1/5+ε≤G≪T, T

Impulsive boundary value problems for p ( t ) -Laplacian’s via critical point theory

Marek Galewski, Donal O'Regan (2012)

Czechoslovak Mathematical Journal

Similarity:

In this paper we investigate the existence of solutions to impulsive problems with a p ( t ) -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order...

An Alternative Form of the Functional Equation for Riemann’s Zeta Function, II

Andrea Ossicini (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for ζ ( s ) . We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function, connected with odd numbers. A proof that Euler himself could have arranged with a little step at the end of his paper “Remarques sur un beau...

Periodic solutions for second order Hamiltonian systems

Qiongfen Zhang, X. H. Tang (2012)

Applications of Mathematics

Similarity:

By using the least action principle and minimax methods in critical point theory, some existence theorems for periodic solutions of second order Hamiltonian systems are obtained.