Generalised quadratic forms over totally real number fields
Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu.
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Author
Browning, Timothy DISTA 
;
Pierce, Lillian B.;
Schindler, Damaris
;
Pierce, Lillian B.;
Schindler, DamarisCorresponding author has ISTA affiliation
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Abstract
We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields.
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Date Published
2024-04-01
Journal Title
Journal of the Institute of Mathematics of Jussieu
Publisher
Cambridge University Press
Acknowledgement
The authors are grateful to Jayce Getz for asking questions that set this project in motion and to the anonymous referee for useful comments. T.B. was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for hosting research visits.
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Cite this
Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. 2024. doi:10.1017/S1474748024000161
Browning, T. D., Pierce, L. B., & Schindler, D. (2024). Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. Cambridge University Press. https://doi.org/10.1017/S1474748024000161
Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised Quadratic Forms over Totally Real Number Fields.” Journal of the Institute of Mathematics of Jussieu. Cambridge University Press, 2024. https://doi.org/10.1017/S1474748024000161.
T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms over totally real number fields,” Journal of the Institute of Mathematics of Jussieu. Cambridge University Press, 2024.
Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu.
Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real Number Fields.” Journal of the Institute of Mathematics of Jussieu, Cambridge University Press, 2024, doi:10.1017/S1474748024000161.
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