Geodesic
On a relation between real and holomorphic functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 68-74.

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We study $\lambda$-holomorphic functions, which generalize holomorphic functions to the case of arbitrary complex exponent $\lambda$. We establish a connection between such functions and real-valued quadratic forms and prove that for $\lambda\ne\mu$, $\lambda\ne\overline{\mu}$ there are $\lambda$- and $\mu$-holomorphic functions whose imaginary parts coincide identically; such functions are polynomials of degree no greater tan two.
Keywords: partial derivative, $\lambda$-holomorphic function, system of algebraic equations, linear substitution, quadratic form.
Mots-clés : Cauchy–Riemann conditions 
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V. G. Nikolaev. On a relation between real and holomorphic functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 68-74. http://geodesic.mathdoc.fr/item/INTO_2021_195_a7/

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