Related papers: Hedgehogs in Lehmer's problem

We provide a proof of the Borwein Conjecture using analytic methods.

In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.

Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable $\mathbb{Z}$-variation of Hodge structures $\mathbb{V}$. Our…

The work studies some Difference equations, which are connected with Mejer's function.

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

For g,n coprime integers, let l_g(n) denote the multiplicative order of g modulo n. Motivated by a conjecture of Arnold, we study the average of l_g(n) as n <= x ranges over integers coprime to g, and x tending to infinity. Assuming the…

We introduce a moving average summability method, which is proved to be equivalent with the logarithmic $\ell$-method. Several equivalence and Tauberian theorems are given. A strong law of large numbers is also proved.

We study atomic measures on $[0,1]$ which are invariant both under multiplication by $2\mod 1$ and by $3\mod 1$, since such measures play an important role in deciding Furstenberg's $\times 2, \times 3$ conjecture. Our specific focus was…

Analogues of Kolmogorov comparison theorems and some of their applications were established.

In the paper, we tackle the following questions: Could the difficulty in solving the Schrodinger equation for an arbitrarily large system be a reflection of some nature intrinsic property? And if so, could this difficulty be a resolution to…

We prove a variety of explicit formulas relating special values of generalized hypergeometric functions to lattice sums with four indices of summation. These results are related to Boyd's conjectured identities between Mahler measures and…

Associated to the Bergman kernels of a polarized toric Kaehler manifold $(M, \omega, L, h)$ are sequences of measures $\{\mu_k^z\}_{k=1}^{\infty}$ parametrized by the points $z \in M$. We determine the asymptotics of the entropies…

Given a finite Borel measure $\mu$ on R n and basic semi-algebraic sets $\Omega$\_i $\subset$ R n , i = 1,. .. , p, we provide a systematic numerical scheme to approximate as closely as desired $\mu$(\cup\_i $\Omega$\_i), when all moments…

A classical theorem of Lusin states that all analytic sets are Lebesgue-measurable. In this article we established the reverse mathematical strength of Lusin's theorem, which depends on how precisely it is formalized. By doing so, we answer…

We strengthen H\"older's inequality. The new family of sharp inequalities we obtain might be thought of as an analog of Pythagorean theorem for the $L^p$ spaces. Our reasonings rely upon Bellman functions of four variables.

We present a completely explicit transcendence measure for $e$. This is a continuation and an improvement to the works of Borel, Mahler and Hata on the topic. Furthermore, we also prove a transcendence measure for an arbitrary positive…

We provide an elementary derivation of the Bessel analog of the celebrated Riesz composition formula and use the former to effortlessly derive the latter.

We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…

Analogical proportions are expressions of the form ``$a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning which itself is at the core of human and artificial intelligence. The author has recently introduced {\em from first…

We establish a new description of the Schur-Agler norm of a holomorphic function on the polydisc as the solution of a convex optimization problem. Consequences of this description are explored both from a theoretical and from a practical…