[2307.10280] Smooth polynomials with several prescribed coefficients Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:2307.10280 (math) [Submitted on 18 Jul 2023 ( v1 ), last revised 21 May 2026 (this version, v6)] Title: Smooth polynomials with several prescribed coefficients Authors: László Mérai View a PDF of the paper titled Smooth polynomials with several prescribed coefficients, by L\'aszl\'o M\'erai View PDF HTML (experimental) Abstract: Let $\mathbb{F}_q[t]$ be the polynomial ring over the finite field $\mathbb{F}_q$ of $q$ elements. A polynomial in $\mathbb{F}_q[t]$ is called $m$-smooth (or $m$-friable) if all its irreducible factors are of degree at most $m$. In this paper, we investigate the distribution of $m$-smooth (or $m$-friable) polynomials with prescribed coefficients. Our technique is based on character sum estimates on smooth (friable) polynomials, Bourgains's argument (2015) applied for polynomials by Ha (2016) and on double character sums on smooth (friable) polynomials. Subjects: Number Theory (math.NT) Cite as: arXiv:2307.10280 [math.NT] (or arXiv:2307.10280v6 [math.NT] for this version) https://doi.org/10.48550/arXiv.2307.10280 Focus to learn more arXiv-issued DOI via DataCite Submission history From: László Mérai [ view email ] [v1] Tue, 18 Jul 2023 10:49:15 UTC (19 KB) [v2] Tue, 11 Jun 2024 11:22:20 UTC (21 KB) [v3] Thu, 14 Aug 2025 10:15:51 UTC (26 KB) [v4] Tue, 10 Mar 2026 11:16:15 UTC (21 KB) [v5] Tue, 28 Apr 2026 08:17:06 UTC (21 KB) [v6] Thu, 21 May 2026 13:58:25 UTC (21 KB) Full-text links: Access Paper: View a PDF of the paper titled Smooth polynomials with several prescribed coefficients, by L\'aszl\'o M\'erai View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2023-07 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from