There are many known asymptotic estimates for the expected number of real zeros of a random algebraic polynomial $a_{0} + a_{1}x + a_{2}x^{2} + \cdot\cdot\cdot + a_{n ...

We prove that if $f(x)=\sum _{k=0}^{n-1}a_{k}x^{k}$ is a polynomial with no cyclotomic factors whose coefficients satisfy $a_{k}$ ≡ 1 mod 2 for 0 ≤ k < n, then ...

Bi-univalent functions constitute a significant subclass of analytic functions defined on the open unit disc, characterised by the property that both the function and its inverse are univalent. This ...