A remark on Zilber's pseudoexponentiation

Henson and Rubel's theorem for Zilber's pseudoexponentiation

In 1984, Henson and Rubel proved the following theorem: If p(x1, ..., xn) is an exponential polynomial with coefficients in C with no zeroes in C, then p(x1, ..., xn) = e g(x1,...,xn) for some exponential polynomial g(x1, ..., xn) over C. In this paper, I will prove the analog of this theorem for Zilber’s Pseudoexponentiation directly from the axioms. Furthermore, this proof relies only on the ...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane

In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.

A short remark on the result of Jozsef Sandor

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.

A remark on the means of the number of divisors

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.