Related papers: A note on Artin's constant
In this paper, we introduce the notion of an Evertse-Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced by the authors in a recent joint paper. We then use it to recover several previously known…
It is proved that the sum of n independent but non-identically distributed doubly truncated Normal distributions converges in distribution to a Normal distribution. It is also shown how the result can be applied in estimating a constrained…
A general formula for bound-continuous transition form factors is derived. It is shown that these form factors can be represented in the form of finite sum of terms with simple analytical structure.
We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a…
This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…
In this paper, for a finite group, we discuss a method for calculating equivariant homology with constant coefficients. We apply it to completely calculate the geometric fixed points of the equivariant spectrum representing equivariant…
Various contributions to the cosmological constant are discussed and confronted with its recent measurement. We briefly review different scenarious -- and their difficulties -- for a solution of the cosmological constant problem.
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the M$\ddot{u}$ntz formula and the Poisson summation formula. By utilizing known properties of Mellin inversion, we give an example from a discontinuous…
We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.
Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer's faithfulness proof for this linear representation to Artin groups of finite type.
The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories.…
We present further results on a class of sums which involve complex powers of the distance to points in a two-dimensional square lattice and trigonometric functions of their angle, supplementing those in a previous paper (McPhedran et al,…
In science, as in life, `surprises' can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of…
We give formulas for the number of representations of non negative integers by various quadratic forms. We also give evaluations in the case of sum of two cubes (cubic case) and the quintic case, as well. We introduce a class of generalized…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
In this short note we prove a result that is an extension of an old Olympiad problem and is a very simple variant of the question of finding an approximation for $k$, where it is a nonzero constant and it satisfies the equation $a^k+b^k=c$,…
We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants $J^{\pm}$ and $\mathit{St}$ behave under the generalized connected…