Related papers: On the Counting Function of Elliptic Carmichael Nu…
We introduce a linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance. Using Hermite interpolation we construct polynomials to derive corresponding…
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.
Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…
For every sufficiently large integer $R$, there exists a Carmichael number with exactly $R$ prime factors.
We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values.
In a previous article the authors determined the best-known upper bound for the cardinality of the image set for several classes of functions, including planar functions. Here, we show that the upper bound cannot be tight for planar…
This note discusses elliptic functions in Ramanujan's work.
Based on new explicit estimates for the prime counting function, we improve the currently known estimates for the particular sequence $C_n = np_n - \sum_{k \leq n}p_k$, $n \geq 1$, involving the prime numbers.
The aim of this work is to provide an upper bound on the eigenvalues counting function $N(\mathbb{R}^n,-\Delta+V,e)$ of a Sch\"odinger operator $-\Delta +V$ on $\mathbb{R}^n$ corresponding to a potential $V\in…
Let $q$ be a power of a prime $p$, let $k$ be a nontrivial divisor of $q-1$ and write $e=(q-1)/k$. We study upper bounds for cyclotomic numbers $(a,b)$ of order $e$ over the finite field $\mathbb{F}_q$. A general result of our study is that…
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature.…
We establish two new estimates which control a function (after subtracting its average) in $L^1$ by only the $L^1$ norm of its radial derivative. While the interior estimate holds for all superharmonic functions, the boundary version is…
The sums of floor functions have been studied by Jacobsthal, Carlitz, Grimson, and Tverberg. More recently, Onphaeng and Pongsriiam proved some sharp upper and lower bounds for the sums of Jacobsthal and Tverberg. In this paper, we devise…
We study the prime number race for elliptic curves over the function field of a proper, smooth and geometrically connected curve over a finite field. This constitutes a function field analogue of prior work by Mazur, Sarnak and the second…
Silverman and Stange defined the notion of an aliquot cycle of length $L$ for a fixed elliptic curve $E/\mathbb{Q}$, and conjectured an order of magnitude for the function that counts such aliquot cycles. We show that the conjectured upper…
This paper explores the application of Hurlbert's Linear Optimization Technique to determine bounds on pebbling numbers. By applying Hurlbert's weight functions and optimization methods, we derive upper bounds for specific graph families.…
The lower bound for the chromatic number of $\mathbb{R}^n$ is improved for $n = 6, 7, 10, 11, 12, 13 \mbox{ and } 14$.
Starting with an infinite set of non linear Equations for the Li-Keiper coefficients, we first specify a lower bound emerging from the infinite set and give a characterization of it. Then, we propose a possible new upper and lower bound for…
We describe two new algorithms for the efficient and rigorous computation of Dirichlet L-functions and their use to verify the Generalised Riemann Hypothesis for all such L-functions associated with primitive characters of modulus…