Lower Bound for p-Adic Exponential Polynomials Evaluated at Some Integer Points

Main Article Content

Vichian Laohakosol
Angkana Sripayap*

Abstract

In 1981, a p-adic interpolation method based on divided differences was derived and was applied to derive, among other things, results on the number of zeros and the bound of certain p-adic exponential polynomials. Here, lower bounds for a p-adic exponential polynomial evaluated over some rational integers are derived using a method of van der Poorten.


Keywords: p-adic exponential polynomial, Turán’s theorem


*Corresponding author:  Tel.:662-5625555 ext 647086


E-mail: [email protected]


 
 

Article Details

Section
Original Research Articles

References

[1] Laohakosol, V. and Pitman, J., 1981. Applications of p-adic interpolation to exponential
polynomials and sum of powers. Journal of Australian Mathematical Society, (Ser. A) 30,
419-437.

[2] van der Poorten, A.J., 1970. Generalisations of Turán’s main theorems on lower bounds
for sums of powers. Bulletin of the Australian Mathematical Society, 2, 15-37.

[3] van der Poorten, A.J., 1976. Some determinants that should be better known. Journal of
Australian Mathematical Society, (Ser. A) 21, 278-288.

[4] Adams, W.W., 1966. Transcendental numbers in the p-adic domain. American Journal of
Mathematics, 88, 279-308.

[5] Turán’s, P., 1953. Eine neue Methode in der Analysis und deren Anwendungen.
Akademiai Kiado: Budapest.

[6] Cassels, J.W.S., 1976. An embedding theorem for fields. Bulletin of the Australian
Mathematical Society, 14, 147-168.

[7] Amice, Y., 1959. Analyse p -adiques. Seminaire Delange-Pisot, 1, 63 pages.