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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 377, Pages 91–110
(Mi znsl3817)
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This article is cited in 2 scientific papers (total in 2 papers)
The circle method with weights for the representation of integers by quadratic forms
N. Niedermowwe Mathematical Institute, Oxford, United Kingdom
Abstract:
When attacking Diophantine counting problems by the circle method, the use of smoothly weighted counting functions has become commonplace to avoid technical difficulties. It can, however, be problematic to then recover corresponding results for the unweighted number of solutions.
This paper looks at quadratic forms in four or more variables representing an integer. We show how an asymptotic formula for the number of unweighted solutions in an expanding region can be obtained despite applying a weighted version of the circle method. Moreover, by carefully choosing the weight, the resulting error term is made non-trivial. Bibl. 9 titles.
Key words and phrases:
Diophantine problem, circle method, weighted counting functions, quadratic forms.
Received: 05.06.2010
Citation:
N. Niedermowwe, “The circle method with weights for the representation of integers by quadratic forms”, Studies in number theory. Part 10, Zap. Nauchn. Sem. POMI, 377, POMI, St. Petersburg, 2010, 91–110; J. Math. Sci. (N. Y.), 171:6 (2010), 753–764
Linking options:
https://www.mathnet.ru/eng/znsl3817 https://www.mathnet.ru/eng/znsl/v377/p91
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Statistics & downloads: |
Abstract page: | 149 | Full-text PDF : | 58 | References: | 44 |
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