skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Gabdullin, Mikhail"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, Transactions of the American Mathematical Society)
    We show that for any polynomial f : Z → Z f:\mathbb {Z}\to \mathbb {Z} with positive leading coefficient and irreducible over Q \mathbb {Q} , if x x is large enough then there is a string of ( log ⁡ x ) ( log ⁡ log ⁡ x ) 1 / 835 (\log x)(\log \log x)^{1/835} consecutive integers n ∈ [ 1 , x ] n\in [1,x] for which f ( n ) f(n) is composite. This improves the result by Kevin Ford, Sergei Konyagin, James Maynard, Carl Pomerance, and Terence Tao [J. Eur. Math. Soc. (JEMS) 23 (2023), pp. 667–700], which has the exponent of log ⁡ log ⁡ x \log \log x being a constant depending on f f which can be exponentially small in the degree of f f . 
    more » « less
    Free, publicly-accessible full text available December 30, 2025
  2. ; (, Proceedings of the American Mathematical Society)
    Full Text Available