Some investigations on uniqueness of entire and meromorphic functions and difference polynomials

Abstract

The Fundamental Theorem of Algebra which tells that a polynomial over C of newlinedegree n must have exactly n roots (counting multiplicities) was one of the most newlinefascinating results of nineteenth century, the study of which started in the early newlineseventeenth century. The theorem can also be stated as: A polynomial over C of newlinedegree n takes the value zero exactly n times. Thus, the distribution of the zeros newlinedetermines a polynomial completely. However, difficulties came in the way when newlinethe general entire functions were taken into consideration instead of polynomials. newlineBorel s works related to the order of growth of entire functions were remarkable newlineadvancement in this regard which enriched the theory which was being developed newlinebased on a number of results due to Picard, Weierstrass, Hadamard and many oth- newlineers. But after a certain stage it became apparent that further development of the newlinearea needed a new theory which finally was provided by Rolf Nevanlinna through newlinea series of publications in the early nineteenth century, called the Nevanlinna The- newlineory. This thesis contains seven chapters dealing with the value distribution and newlineuniqueness of entire and meromorphic functions using the notion of Nevanlinna newlineTheory. The first chapter is the introductory chapter containing basic definitions newlineand important results, some of which we state here. newline