# On the representation of integers by quadratic forms

Browning TD, Dietmann R. 2008. On the representation of integers by quadratic forms. Proceedings of the London Mathematical Society. 96(2), 389–416.

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*Journal Article*|

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Author

Browning, Timothy D

^{IST Austria}^{}; Dietmann, RainerAbstract

Let n ≥ 4 and let Q ∈ [X1, ..., Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.

Publishing Year

Date Published

2008-03-01

Journal Title

Proceedings of the London Mathematical Society

Volume

96

Issue

2

Page

389 - 416

IST-REx-ID

### Cite this

Browning TD, Dietmann R. On the representation of integers by quadratic forms.

*Proceedings of the London Mathematical Society*. 2008;96(2):389-416. doi:10.1112/plms/pdm032Browning, T. D., & Dietmann, R. (2008). On the representation of integers by quadratic forms.

*Proceedings of the London Mathematical Society*. John Wiley and Sons Ltd. https://doi.org/10.1112/plms/pdm032Browning, Timothy D, and Rainer Dietmann. “On the Representation of Integers by Quadratic Forms.”

*Proceedings of the London Mathematical Society*. John Wiley and Sons Ltd, 2008. https://doi.org/10.1112/plms/pdm032.T. D. Browning and R. Dietmann, “On the representation of integers by quadratic forms,”

*Proceedings of the London Mathematical Society*, vol. 96, no. 2. John Wiley and Sons Ltd, pp. 389–416, 2008.Browning, Timothy D., and Rainer Dietmann. “On the Representation of Integers by Quadratic Forms.”

*Proceedings of the London Mathematical Society*, vol. 96, no. 2, John Wiley and Sons Ltd, 2008, pp. 389–416, doi:10.1112/plms/pdm032.