GENERALISED QUADRATIC FORMS OVER TOTALLY REAL NUMBER FIELDS

T. D. Browning, Lillian B. Pierce, Damaris Schindler

Type: Article

Publication Date: 2024-04-11

Citations: 0

DOI: https://doi.org/10.1017/s1474748024000161

Abstract

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.

Locations

Journal of the Institute of Mathematics of Jussieu - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (10)

Action	Title	Year	Authors
+ PDF Chat	A new form of the circle method, and its application to quadratic forms.	1996	D. R. Heath‐Brown
+ PDF Chat	Simultaneous integer values of pairs of quadratic forms	2015	D. R. Heath‐Brown Lillian B. Pierce
+	Lectures on the Theory of Algebraic Numbers	1981	E. Hecke
+ PDF Chat	Non-Homogeneous Cubic Equations	1964	H. Davenport D. J. Lewis
+	Rational points on nonsingular cubic hypersurfaces	1994	Christopher Skinner
+ PDF Chat	None	1997	C. M. SKINNER
+ PDF Chat	Quadratic forms and systems of forms in many variables	2018	Simon L. Rydin Myerson
+	Bounds for automorphicL-functions	1993	William Duke John Friedlander Henryk Iwaniec
+ PDF Chat	Cubic hypersurfaces and a version of the circle method for number fields	2014	T. D. Browning Pankaj Vishe
+	Algebraic Number Theory	1986	Serge Lang