We prove that the homogeneously polyanalytic functions of total order m, defined by system equations $$\overline{D}^{(k_1,\ldots ,k_n)} f=0$$ with $$k_1+\cdots +k_n=m$$ , can be written as polynomials degree $$<m$$ in variables $$\overline{z_1},\ldots ,\overline{z_n}$$ some analytic coefficients. establish a weighted mean value property for such functions, using reproducing Jacobi polynomials. ...

In this paper we construct and prove superintegrability of spin Calogero-Moser type systems on symplectic leaves K 1 <mml:mi class="MJX-v...

We consider intersections of $n$ diagonal forms degrees $k_1 \lt \cdots k_n$, and we prove an asymptotic formula for the number rational points bounded height on these varieties. The proof uses Hardy–Littlewood method recent breakthro

We prove that linear groups over rings of non-commutative Laurent polynomials $D_{\tau}$ have Tits systems with the corresponding affine Weyl and universal central extensions if $|Z(D)|\geq 5$ $|Z(D)|\neq 9$. also determine structures $K_1$-groups identify generators $K_2$-groups.

Digital signature schemes in general and representative collective digital schemes, particular, are often built based on the difficulty of discrete logarithm problem finite field, elliptic curve, factor analysis, finding roots modulo large primes or a combination difficult problems mentioned above. In this paper, we use new problem, which is to find with root ground field GF(p) build but chosen...

For a partition $$\varvec{k} = (k_1, \dots , k_m)$$ of n consider the group $$\mathrm {U}(\varvec{k}) \mathrm {U}(k_1) \times {U}(k_m)$$ block diagonally embedded in {U}(n)$$ and center $$\mathbb {T}^m$$ {U}(\varvec{k})$$ . We study Toeplitz operators with -invariant symbols acting on weighted Bergman spaces unit ball {B}^n$$ introduce $$(\varvec{k},j)$$ -quasi-radial quasi-homogeneous as those...