Keywords:-

Keywords: zeros of p-adic meromorphic functions , derivative , Wronskian .

Article Content:-

Abstract

Let  be an algebraically closed field of characteristic 0, complete with respect to an ultrametric absolute value. Showed that by Kamal Boussaf , Alain Escassut and Jacqueline Ojeda  [1]  if the Wronskian of two entire functions in is apolynomial, then both functions are polynomials. As a consequence, if  meromorphic sequence of functions  on all  is transcendental and has finitely many multiple poles,  then  takes all values in  infinitely many times. Then study applications to  meromorphic sequence of functions   has finitely many zeros, aproblem linkedtothe Hayman conjecture on adic field.

References:-

References

Kamal Boussaf, Alain Escassut, Jacqueline Ojeda : Zeros of the derivative of p-adic meromorphic functions and applications . Bull. Belg. Math. Soc. Simon , 19(2012), 367-372

A. Escassut : p-adic Value Distribution. Some Topicson Value Distribution and Differentiability in Complex and p-adic cAnalysis .MathematicsMonograph,. Science Press , pp42-138 . 2008 .

P.C. Hu and C. C yang : Meromorphic function over non-Archimedeam fields. Kluwer Academic publishers (2000)

J. Ojeda :distribution de valeurs des functions meromorphes ultrametrique, applications de la theorie de Nevanlina. ,Univesite Blaise Pascal, Clermont-Ferrand, France (2008).

W. Bergweiler and X. C.:Pang on the derivative of meromorphic functions unih. Multiple zeros . J. Math. Anal. Appl. 278, pp. 285-292 (2003).

Boussaf Picard : values of p-adic meromorphic function. p-adic Numbers, Ul- trimetric Analysis and Applications. Vol. 2, N. 4, pp. 285-292 (2010)

A. Escassut andJ. Ojeda : Exceptional values of p-adic analytic functions and derivatives. Complex Variables and Elliptic Equations. Vol 56, N. -4, pp. 263-269 (2011).

J. Ojeda : Hyman’s conjecture over a p-adic field , Taiwanese Journal of mathematics. Vol. 12, N. 9, pp.2295-2313 (2008).

k(. Boussaf and J. Ojeda Value distribution of p-adic meromorphic functions, Bul- letin of the Belgian Mathematical Society - Simon Stevin, Vol 18, n.4, P: 667-678 (2011).

Escassut, A. : Analytic Elements in p-adic Analysis. World Scientific Publishing Co. Pte.Ltd. (Singapore, 1995).

Downloads

Citation Tools

How to Cite
Mustafa, M., Joseph, S., & Dawood, A. (2019). Derivative of Adic Meromorphic Function and Their Applications. International Journal Of Mathematics And Computer Research, 7(04), 1951-1953. https://doi.org/10.31142/ijmcr/v7i04.01