On the number of zeros of exponential polynomials and related questions

A. J. van der Poorten, Igor E. Shparlinski

Type: Article

Publication Date: 1992-12-01

Citations: 14

DOI: https://doi.org/10.1017/s0004972700012065

Abstract

We apply Straßmann's theorem to p –adic power series satisfying linear differential equations with polynomial coefficients and note that our approach leads to our estimating the number of integer zeros of polynomials on a given interval and thence to an investigation of the number of p –adic small values of a function on such an interval, that is, of the number of solutions of a congruence modulo p r .

Locations

Bulletin of the Australian Mathematical Society - View - PDF

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Action	Title	Year	Authors
+ PDF Chat	Counting the values taken by algebraic exponential polynomials	1999	Graham Everest Igor E. Shparlinski
+	Bernstein Type Inequalities for Quasipolynomials	2001	Alexander Brudnyi
+	Möbius Randomness Law for Frobenius Traces of Ordinary Curves	2020	Min Sha Igor E. Shparlinski
+	Zero testing of p-adic and modular polynomials	2000	Marek Karpiński Alf van der Poorten Igor E. Shparlinski
+	Sums of multiplicative coefficients twisted by Frobenius traces	2023	Yuxuan Zhou
+ PDF Chat	Explicit Form of Cassels’<i>p</i>-adic Embedding Theorem for Number Fields	2015	Artūras Dubickas Min Sha Igor E. Shparlinski
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+	Some divisibilities amongst the terms of linear recurrences	2006	Florian Luca Igor E. Shparlinski
+ PDF Chat	On linear recurrence sequences with polynomial coefficients	1996	A. J. van der Poorten Igor E. Shparlinski
+	On Certain Exponential Sums and the Distribution of Diffie-Hellman Triples	1999	Ran Canetti John Friedlander Igor E. Shparlinski

Works Cited by This (8)

Action	Title	Year	Authors
+	Zeros of <i>p</i> -Adic Exponential Polynomials II	1987	A. J. van der Poorten Robert Rumely
+	Number of different prime divisors of recurrence sequences	1987	Igor E. Shparlinski
+ PDF Chat	An embedding theorem for fields	1976	J. W. S. Cassels
+ PDF Chat	Additive relations in fields	1991	A. J. van der Poorten Hans Peter Schlickewei
+	On the number of zeros of certain functions	1975	Marc Voorhoeve A. J. van der Poorten R. Tijdeman
+	Zeros of p-adic exponential polynomials	1976	A. J. van der Poorten
+ PDF Chat	Zeros of recurrence sequences	1991	A. J. van der Poorten Hans Peter Schlickewei
+ PDF Chat	Computational Number Theory	1991	Attila Pethő Michael Pohst Hugh C. Williams Horst Günter Zimmer