Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivated by previous work on the simplification of parametrizations of curves, in this paper  generalize the ll-known notion of analytic polynomial (a bivariate polynomial P(x, y), with complex coefficients, which arises by substituting z→x+iy on a univariate polynomial p(z)∈ℂ[z], i.e. p(z)→p(x+iy)=P(x, y)) to other finite field extensions, beyond the classical case of ℝ⊂ℂ. In this general setting  obtain different properties on the factorization, gcd's and resultants of analytic polynomials, which seem to be new even in the context of Complex Analysis. Moreover,  extend the ll-known Cauchy–Riemann conditions (for harmonic conjugates) to this algebraic framework, proving that the new conditions also characterize the components of generalized analytic polynomials.
['Tomás Recio', 'J. Rafael Sendra', 'Luis Felipe Tabera', 'Carlos Villarino']
I am writing a research paper on a idea Factoring analytic multivariate polynomials and non-standard Cauchy–Riemann conditions
[{"from": "human", "value": "I am writing a research paper on a idea Factoring analytic multivariate polynomials and non-standard Cauchy\u2013Riemann conditions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivated by previous work on the simplification of parametrizations of curves, in this paper  generalize the ll-known notion of analytic polynomial (a bivariate polynomial P(x, y), with complex coefficients, which arises by substituting z\u2192x+iy on a univariate polynomial p(z)\u2208\u2102[z], i.e. p(z)\u2192p(x+iy)=P(x, y)) to other finite field extensions, beyond the classical case of \u211d\u2282\u2102. In this general setting  obtain different properties on the factorization, gcd's and resultants of analytic polynomials, which seem to be new even in the context of Complex Analysis. Moreover,  extend the ll-known Cauchy\u2013Riemann conditions (for harmonic conjugates) to this algebraic framework, proving that the new conditions also characterize the components of generalized analytic polynomials."}]