Algorithmic Arithmetic Fewnomial Theory I: One Variable
Ashraf Ibrahim, J. Maurice Rojas, Korben Rusek
TL;DR
This paper discusses the initial development of a theory related to arithmetic fewnomials in one variable, but the main proof was withdrawn due to an error involving prime avoidance in finite fields.
Contribution
The paper introduces a new theoretical framework for arithmetic fewnomials in one variable, aiming to extend existing algebraic methods.
Findings
The proof of Theorem 1.5 was withdrawn due to an error.
The initial theory was incomplete and requires correction.
No concrete results are confirmed due to the withdrawal.
Abstract
Withdrawn by the authors due to an error in the proof of the finite field result (Thm. 1.5): The random primes used in the proof need NOT avoid the exceptional primes from Lemma 2.7, thus leaving Thm. 1.5 unproved.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Coding theory and cryptography