Related papers: Some Sufficient Conditions for the Riemann hypothe…
In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.
In this short article we obtain some necessary conditions for a so-called fractional Hardy-Sobolev's inequalities in multidimensional case. We also give some examples to show the sharpness of these inequalities.
This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…
We prove under RH the existence of a very large positive and negative values of the argument of the Riemann zeta function on a very short intervals.
In this paper we provide a short proof of the Riemann Hypothesis for Drinfeld modules which uses only basic notions from the theory of global function fields and of Drinfeld modules.
This article provides a proof of the famous \textit{Prime Number Theorem} by establishing an analogous statement of the same in terms of the second \textit{Chebyshev Function} $\psi(x)$. We shall be extensively using complex analytic…
We consider Mertens' function M(x,q,a) in arithmetic progression, Assuming the generalized Riemann hypothesis (GRH), we show an upper bound that is uniform for all moduli which are not too large. For the proof, a former method of K.…
Assuming the Generalised Riemann Hypothesis, we prove a sharp upper bound on moments of shifted Dirichlet $L$-functions. We use this to obtain conditional upper bounds on high moments of theta functions. Both of these results strengthen…
The main result of this paper provides six necessary and sufficient conditions under various regularity assumptions for a so-called Cauchy mean to be identical to a two-variable quasiarithmetic mean. One of these conditions says that a…
In this paper a hyperbolic system of partial differential equations for two-phase mixture flows with $N$ components is studied. It is derived from a more complicated model involving diffusion and exchange terms. Important features of the…
Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations between hypothetical error terms in the asymptotic formulae for truncated mean-square average of exponential sums over primes and in the…
We consider the approximation of a continuous function, defined on a compact set of the $d$-dimensional Euclidean space, by sums of two ridge functions. We obtain a necessary and sufficient condition for such a sum to be a best…
We discuss some properties of conditional expectation operators, and use these facts to prove an interesting counterexample regarding sufficient statistics. In particular, we show that there exists sufficient random variables X and Y, such…
We derive sufficient conditions for theories consisting of multiple vector fields, which could also couple to external fields, to be multi-field generalised Proca theories. The conditions are derived by demanding that the theories have the…
We study the system of root functions (SRF) of Hill operator $Ly = -y^{\prime \prime} +vy $ with a singular potential $v \in H^{-1}_{per}$ and SRF of 1D Dirac operator $ Ly = i {pmatrix} 1 & 0 0 & -1 {pmatrix} \frac{dy}{dx} + vy $ with…
There are various situations in which it is natural to ask whether a given collection of $k$ functions, $\rho_j(\r_1,...,\r_j)$, $j=1,...,k$, defined on a set $X$, are the first $k$ correlation functions of a point process on $X$. Here we…
In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.
A hyperplane arrangement is said to satisfy the ``Riemann hypothesis'' if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley for certain families of arrangements which…
Riemann conjectured that all the zeros of the Riemann $\Xi$-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums $\Xi_N(z)$ in Riemann's uniformly…
The Riemann-Lebesque Theorem is commonly proved in a few strokes using the theory of Lebesque integration. Here, the upper bound $2\pi|c_k(f)|\le S_k(f)-s_k(f)$ for the Fourier coefficients $c_k$ is proved in terms of majoring and minoring…