Infinitude of palindromic almost-prime numbers
Aleksandr Tuxanidy, Daniel Panario
TL;DR
This paper proves that in any base, there are infinitely many palindromic numbers with at most six large prime divisors, using advanced equidistribution estimates and bounds on exponential sums.
Contribution
It introduces new equidistribution estimates for palindromes in residue classes and provides bounds on moments related to exponential sums over palindromes.
Findings
Infinitely many palindromic numbers with limited prime divisors exist in any base.
New bounds for moments and averages of products related to exponential sums over palindromes.
Establishment of equidistribution estimates for palindromes in residue classes.
Abstract
It is proven that, in any given base, there are infinitely many palindromic numbers having at most six prime divisors, each relatively large. The work involves equidistribution estimates for the palindromes in residue classes to large moduli, offering upper bounds for moments and averages of certain products closely related to exponential sums over palindromes
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Taxonomy
TopicsAnalytic Number Theory Research · Mathematical Approximation and Integration