On the distribution of Dedekind sums
Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it highlights results about the values of Dedekind sums, their...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2018-12-01
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| Series: | Surveys in Mathematics and its Applications |
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| Online Access: | http://www.utgjiu.ro/math/sma/v13/p13_15.pdf |
| _version_ | 1818877550499201024 |
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| author | Kurt Girstmair |
| author_facet | Kurt Girstmair |
| author_sort | Kurt Girstmair |
| collection | DOAJ |
| description | Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest.
This article gives a survey of several aspects of the distribution of these sums. In particular, it highlights results
about the values of Dedekind sums, their density and uniform distribution. Further topics include mean values,
large and small (absolute) values, and the behaviour of Dedekind sums near quadratic irrationals.
The present paper can be considered as a supplement to the survey article [R. W. Bruggeman, On the distribution of Dedekind sums, Contemp. Math. 166 (1994), 197--210]. |
| first_indexed | 2024-12-19T14:00:04Z |
| format | Article |
| id | doaj.art-646bf56464a0470a8649cc9fe637d421 |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-12-19T14:00:04Z |
| publishDate | 2018-12-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-646bf56464a0470a8649cc9fe637d4212022-12-21T20:18:29ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982018-12-0113 (2018)251263On the distribution of Dedekind sumsKurt Girstmair0Institut für Mathematik, Universität Innsbruck, Technikerstr. 13/7 A-6020 Innsbruck, Austria.Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it highlights results about the values of Dedekind sums, their density and uniform distribution. Further topics include mean values, large and small (absolute) values, and the behaviour of Dedekind sums near quadratic irrationals. The present paper can be considered as a supplement to the survey article [R. W. Bruggeman, On the distribution of Dedekind sums, Contemp. Math. 166 (1994), 197--210].http://www.utgjiu.ro/math/sma/v13/p13_15.pdfDedekind sumsdistribution of Dedekind sums |
| spellingShingle | Kurt Girstmair On the distribution of Dedekind sums Surveys in Mathematics and its Applications Dedekind sums distribution of Dedekind sums |
| title | On the distribution of Dedekind sums |
| title_full | On the distribution of Dedekind sums |
| title_fullStr | On the distribution of Dedekind sums |
| title_full_unstemmed | On the distribution of Dedekind sums |
| title_short | On the distribution of Dedekind sums |
| title_sort | on the distribution of dedekind sums |
| topic | Dedekind sums distribution of Dedekind sums |
| url | http://www.utgjiu.ro/math/sma/v13/p13_15.pdf |
| work_keys_str_mv | AT kurtgirstmair onthedistributionofdedekindsums |