Related papers: On arithmetical nature of Tichy-Uitz's function
For the natural two parameter filtration $(\mathcal{F}_\lambda : \lambda \in P)$ on the boundary of a triangle building we define a maximal function and a square function and show their boundedness on $L^p(\Omega_0)$ for $p \in (1,…
We introduce a self-inverse function via an integral equivalent to a two-term combination of dilogarithms. We refer to this function as a fundamental form, since there is a family of extensions of this function that satisfy similar…
We introduce the edge Schur functions $E^{\lambda}$ that are defined as a generating series over edge labeled tableaux. We formulate $E^{\lambda}$ as the partition function for a solvable lattice model, which we use to show they are…
Beginning in 2006, G. Gentili and D.C. Struppa developed a theory of regular quaternionic functions with properties that recall classical results in complex analysis. For instance, in each Euclidean ball centered at 0 the set of regular…
We define a new quasiregular mapping T in three dimensions that generalizes the tangent function on the complex plane and shares a number of its geometric properties. We investigate the dynamics of the family \lambda T for \lambda>0,…
It is well known that if one integrates a Schur function indexed by a partition $\lambda$ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of $\lambda$ have even multiplicity (resp. all parts of $\lambda$…
The objective of this paper is to show (a)=(b)=(c) as rational functions of $T$, $U$ for (a), (b), (c) given by (a) continued fractions of length $2^{n+1}-1$ with explicit partial denominators in $\left\{-T,U^{-1}T\right\}$, (b) truncated…
We prove that the pattern matching problem is undecidable in polymorphic lambda-calculi (as Girard's system F) and calculi supporting inductive types (as G{\"o}del's system T) by reducing Hilbert's tenth problem to it. More generally…
The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi-Trudi formula and the Lascoux-Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of…
Let $M(\alpha)$ denote the (logarithmic) Mahler measure of the algebraic number $\alpha$. Dubickas and Smyth, and later Fili and the author, examined metric versions of $M$. The author generalized these constructions in order to associate,…
In 2005, Abramsky introduced various linear/affine combinatory algebras of partial involutions over a suitable formal language, to discuss reversible computation in a game-theoretic setting. These algebras arise as instances of the general…
Fixing an arithmetic lattice $\Gamma$ in an algebraic group $G$, the commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $\Delta$ with $[\Gamma : \Gamma \cap \Delta] [\Delta: \Gamma \cap \Delta] =…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
In \cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\cdots]$ using Teichm\"{u}ller character of finite fields and quotients of $p$-adic gamma function, and expressed the trace of Frobenius of elliptic curves in terms of special…
The family of Cauchy transforms \[C_{g}(z,w) = -\frac{1}{\pi}\int_{\mathbb{C} } \frac{g(u)}{\overline{u-w} (u-z) } da(u ),\] where the measurable function $g$ with compact (essential) support satisfies $0 \leq g\leq 1,$ and suitably defined…
A combinatorial expression for the coefficient of the Schur function $s_{\lambda}$ in the expansion of the plethysm $p_{n/d}^d \circ s_{\mu}$ is given for all $d$ dividing $n$ for the cases in which $n=2$ or $\lambda$ is rectangular. In…
By treating the multiple argument identity of the logarithm of the Gamma function as a functional equation, we obtain a curious infinite product representation of the $sinc$ function in terms of the cotangent function. This result is…
Haglund's conjecture states that $\dfrac{\langle J_{\lambda}(q,q^k),s_\mu \rangle}{(1-q)^{|\lambda|}} \in \mathbb{Z}_{\geq 0}[q]$ for all partitions $\lambda,\mu$ and all non-negative integers $k$, where $J_{\lambda}$ is the integral form…
We consider a Laurent series defined by infinite products $g_u(t) = \prod_{n=0}^\infty (1 + ut^{-2^n})$, where $u\in \mathbb{F}$ is a parameter and $\mathbb{F}$ is a field. We show that for all $u\in\mathbb{Q}\setminus\{-1,0,1\}$ the series…
Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in…