Related papers: Boolean constant degree functions on the slice are…
The graphs of Okamoto's functions, denoted by $K_q$, are self-affine fractal curves contained in $[0,1]^2$, parameterised by $q \in (1,2)$. In this paper we consider the cardinality and dimension of the intersection of these curves with…
For polynomials, local connectivity of Julia sets is a much-studied and important property. Indeed, when the Julia set of a polynomial of degree $d\geq 2$ is locally connected, the topological dynamics can be completely described as a…
We give a classification of the degrees of the points with rational $j$-invariant on the modular curves $X_{0}(n)$ and $X_{1}(n)$. The degrees which occur infinitely often are computed unconditionally, while those which occur finitely often…
We consider the volume of a Boolean expression of some congruent balls about a given system of centers in the $d$-dimensional Euclidean space. When the radius $r$ of the balls is large, this volume can be approximated by a polynomial of…
We suggest an upper bound on binomial coefficients that holds over the entire parameter range and whose form repeats the form of the de Moivre-Laplace approximation of the symmetric binomial distribution. Using the bound, we estimate the…
A Boolean function $f:\{0,1\}^d \mapsto \{0,1\}$ is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make…
We study the recently introduced boolean-width of graphs. Our structural results are as follows. Firstly, we show that almost surely the boolean-width of a random graph on $n$ vertices is $O(\log^2 n)$, and it is easy to find the…
We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of polynomial threshold functions. More specifically, for a Boolean function f on n variables equal to the sign of a real, multivariate polynomial…
We consider negabent Boolean functions that have Trace representation. We completely characterize quadratic negabent monomial functions. We show the relation between negabent functions and bent functions via a quadratic function. Using this…
We prove a Julia inequality for bounded non-commutative functions on polynomial polyhedra. We use this to deduce a Julia inequality for holomorphic functions on classical domains in $\mathbb{C}^d$. We look at differentiability at a boundary…
The Stieltjes constants $\gamma_k(a)$ appear in the regular part of the Laurent expansion of the Hurwitz zeta function about its only polar singularity at $s=1$. We present multi-parameter summation relations for these constants that result…
Holomorphic Cliffordian functions of order $k$ are functions in the kernel of the differential operator $\overline{\partial}\Delta^k$. When $\overline{\partial}\Delta^k$ is applied to functions defined on the paravector space of some…
The 93 minions of Boolean functions stable under left composition with the clone of self-dual monotone functions are described. As an easy consequence, all $(C_1,C_2)$-stable classes of Boolean functions are determined for an arbitrary…
In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in…
We show that the Hilbert-Kunz density function of a quadric hypersurface of Krull dimension $n+1$ is a piecewise polynomial on a subset of $[0, n]$, whose complement in $[0, n]$ has measure zero. Our explicit description of the Hilbert-Kunz…
We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…
Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators.…
We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of independent functions on mutually exclusive subsets of the variables. We prove that any such function is close to just a single function on a single subset. We also…
In this paper, by introducing a new operation in the vector space of analytic functions, the author presents a method for derivating the well-known formulas: $\zeta(1-k)=-\frac{B_k}{k}$ and $\zeta(1-n,a)=-\frac{B_n(a)}{n}$ , where $\zeta$,…
Let $d(n)$ be the number of divisors of $n$, let $$ \Delta(x) := \sum_{n\le x}d(n) - x(\log x + 2\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\zeta(s)$ denote the Riemann zeta-function. Several…