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A two dimensional delta symbol method and applications

Appears in collection : Prime numbers and arithmetic randomness / Nombres premiers et aléa arithmétique

The delta symbol developed by Duke-Friedlander-Iwaniec and Heath-Brown has played an important role in studying rational points on hypersurfaces of low degrees. We present a two dimensional delta symbol and apply it to establish a quantitative Hasse principle for a smooth intersection of two quadratic forms defined over $Q$ in at least ten variables. The goal of these delta symbols is to carry out a (double) Kloosterman refinement of the circle method. This is based on a joint work with Simon Rydin Myerson and Pankaj Vishe.

Information about the video

Date of recording 24/06/2025
Date of publication 15/07/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20368003
Cite this video Li, Junxian (24/06/2025). A two dimensional delta symbol method and applications. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20368003
URL https://dx.doi.org/10.24350/CIRM.V.20368003

Domain(s)

Number Theory

Bibliography

LI, Junxian, MYERSON, Simon L. Rydin, et VISHE, Pankaj. A two-dimensional delta symbol method and its application to pairs of quadratic forms. arXiv preprint arXiv:2411.11355, 2024. - https://doi.org/10.48550/arXiv.2411.11355

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