Lecture Room B, 4th Floor, The 3rd General Building, NTHU

(清華大學綜合三館 4樓B演講室)

The Quotient Problem for Entire Functions

Ji Guo (National Tsing Hua University)

Abstract:

Let

and

be linear recurrence sequences. It is a well-known Diophantine problem to decide the finiteness of the set

of natural numbers such that their ratio

is an integer. In this paper we study an analogue of such a divisibility problem in the complex situation.

Namely,

we are concerned with the divisibility problem (in the sense of complex entire functions) for two sequences

and

, where the

and

are nonconstant entire functions and the

and

are non-zero constants except that

can be zero. We will show that the set

of natural numbers such that

is an entire function is finite under the assumption that

is not constant for any non-trivial index set

.