Imaginary quadratic fields with class group exponent 5
We show that there are finitely many imaginary quadratic number fields for which the class group has exponent 5. Indeed there are finitely many with exponent at most 6. The proof is based on a method of Pierce [13]. The problem is reduced to one of counting integral points on a certain affine surfac...
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| Format: | Journal article |
| Language: | English |
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2008
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| _version_ | 1797059580712189952 |
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| author | Heath-Brown, D |
| author_facet | Heath-Brown, D |
| author_sort | Heath-Brown, D |
| collection | OXFORD |
| description | We show that there are finitely many imaginary quadratic number fields for which the class group has exponent 5. Indeed there are finitely many with exponent at most 6. The proof is based on a method of Pierce [13]. The problem is reduced to one of counting integral points on a certain affine surface. This is tackled using the author's "square-sieve", in conjunction with estimates for exponential sums. The latter are derived using the q-analogue of van der Corput's method. © Walter de Gruyter 2008. |
| first_indexed | 2024-03-06T20:06:21Z |
| format | Journal article |
| id | oxford-uuid:29078c90-dae0-4fa6-9d80-8342abb2b340 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:06:21Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:29078c90-dae0-4fa6-9d80-8342abb2b3402022-03-26T12:16:35ZImaginary quadratic fields with class group exponent 5Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:29078c90-dae0-4fa6-9d80-8342abb2b340EnglishSymplectic Elements at Oxford2008Heath-Brown, DWe show that there are finitely many imaginary quadratic number fields for which the class group has exponent 5. Indeed there are finitely many with exponent at most 6. The proof is based on a method of Pierce [13]. The problem is reduced to one of counting integral points on a certain affine surface. This is tackled using the author's "square-sieve", in conjunction with estimates for exponential sums. The latter are derived using the q-analogue of van der Corput's method. © Walter de Gruyter 2008. |
| spellingShingle | Heath-Brown, D Imaginary quadratic fields with class group exponent 5 |
| title | Imaginary quadratic fields with class group exponent 5 |
| title_full | Imaginary quadratic fields with class group exponent 5 |
| title_fullStr | Imaginary quadratic fields with class group exponent 5 |
| title_full_unstemmed | Imaginary quadratic fields with class group exponent 5 |
| title_short | Imaginary quadratic fields with class group exponent 5 |
| title_sort | imaginary quadratic fields with class group exponent 5 |
| work_keys_str_mv | AT heathbrownd imaginaryquadraticfieldswithclassgroupexponent5 |