Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions

[2608.27732] Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions Skip to main content Search Submit Donate Log in Mathematics > Number Theory arXiv:2608.27732 (math) [Submitted on 27 Aug 2026] Title: Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions Authors: Thomas Wright View PDF HTML (experimental) Abstract: This paper broadens the range on which Fouvry and Radziwiłł's results on nearly balanced convolutions apply. In particular, let $\alpha_m$ and $\beta_n$ be sequences supported on $m\sim M$ and $n\sim N$ where $\beta_n$ is equidistributed for small moduli, and let $Q=X^{\frac 12+\varepsilon}$. We find that \begin{gather*}\sum_{q\sim Q}\left|\mathop{\sum\sum}_{\substack{n\sim N,m\sim M \\ mn\equiv a\pmod q}}\alpha_m\beta_n-\frac{1}{\phi(q)}\mathop{\sum\sum}_{\substack{n\sim N,m\sim M \\ (mn,q)=1}}\alpha_m\beta_n\right|\ll \frac{X}{\log^A X} \end{gather*} if $N=X^{\frac 12+\delta}$ and $M=X^{\frac 12-\delta}$ with $0<\delta<\frac 1{68}$, which improves Fouvry and Radziwiłł's $0<\delta<\frac 1{112}$. To prove this, we sharpen Bettin and Chandee's famous result on trilinear forms with Kloosterman fractions in the case where some of the sums are over subdyadic intervals. Subjects: Number Theory (math.NT) MSC classes: 11L05, 11N37 Cite as: arXiv:2608.27732 [math.NT] (or arXiv:2608.27732v1 [math.NT] for this version) https://doi.org/10.48550/arXiv.2608.27732 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Thomas Wright [ view email ] [v1] Thu, 27 Aug 2026 21:46:09 UTC (9 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

Related documents

• Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions#779654
• An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms#1050934
• Exponential Growth of Mean Multiplicities in Length Spectra of Semi-Arithmetic Surfaces of Arbitrary Arithmetic Dimension#1142768
• Lower Bounds for Moments of Automorphic L-functions#1117004
• Neun Siegel, ein Brudi, kein Plan B / Geminus Klar#658569