Related papers: A Riemann-Farey Computation

We establish upper bounds for shifted moments of modular $L$-functions to a fixed modulus as well as quadratic twists of modular $L$-functions under the generalized Riemann hypothesis. Our results are then used to establish bounds for…

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described.…

We obtain a tight, up to a logarithmic factor, upper bound on the number of solutions to the equation $$ \sum_{j=1}^n a_j \frac{s_j}{r_j} =a_0, \qquad $$ with variables $r_1,...,r_n$ in an arbitrary box at the origin and variables $s_1,...,…

In this short note we derive, for bounded domains, an upper bound for a Friedrichs type constant in a weighted Friedrichs type inequality. This upper bound generalizes a well known upper bound of the Friedrichs constant. This upper bound is…

We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various…

In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also…

We construct a measure on the well-approximable numbers whose Fourier transform decays at a nearly optimal rate. This gives a logarithmic improvement on a previous construction of Kaufman.

We study in an explicit manner the partial sums of the multiplicative inverse of the Riemann zeta function and its derivative.

We revisit the eigenvalue problem of the Dirichlet Laplacian on bounded domains in complete Riemannian manifolds. By building on classical results like Li-Yau's and Yang's inequalities, we derive upper and lower bounds for eigenvalues. For…

Improved model independent upper bounds on the weak transition form factors are derived using inclusive sum rules. Comparison of the new bounds with the old ones is made for the form factors h_{A_1} and h_V in B -> D* decays.

A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.

Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for $\left|\zeta(s)\right|$ right to the critical line. As an application we make explicit Titchmarsh's conditional bound for the Mertens function and…

We consider several differential-topological invariants of compact 4-manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta, we compute these invariants in many cases that were…

We establish upper bounds for the joint moments of the $2k^{\text{th}}$ power of the Riemann zeta function with the $2h^{\text{th}}$ power of its derivative for $0 \leq h \leq 1$ and $1 \leq k \leq 2$. These bounds are expected to be sharp…

We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a…

Lower bounds for some explicit decision problems over the complex numbers are given.

This article will prove a theorem for the existence of k-factor for k>1 ,and present an efficient algorithm for computing k-factor for all values of k based on this theorem.

Let $\mu(n)$ be the M\"{o}bius function and $e(\alpha)=e^{2\pi i\alpha}$. In this paper, we study upper bounds of the classical sum $$S(x,\alpha):=\sum_{1\leq n\leq x}\mu(n)e(\alpha n).$$ We can improve some classical results of Baker and…

In this paper we investigate problems on almost everywhere convergence of subsequences of Riemann sums \md0 R_nf(x)=\frac{1}{n}\sum_{k=0}^{n-1}f\bigg(x+\frac{k}{n}\bigg),\quad x\in \ZT. \emd We establish a relevant connection between…