On the average value of divisor sums in arithmetic progressions
We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that ``on average'' these sums are close to the expected value. We also give applications of our result to sums of the divisor function twisted with characters (both additive a...
| Main Authors: | , , |
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| Format: | Journal article |
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2005
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| _version_ | 1826303695298494464 |
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| author | Heath-Brown, D Banks, W Shparlinski, I |
| author_facet | Heath-Brown, D Banks, W Shparlinski, I |
| author_sort | Heath-Brown, D |
| collection | OXFORD |
| description | We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that ``on average'' these sums are close to the expected value. We also give applications of our result to sums of the divisor function twisted with characters (both additive and multiplicative) taken on the values of various functions, such as rational and exponential functions; in particular, we obtain upper bounds for such twisted sums. |
| first_indexed | 2024-03-07T06:06:37Z |
| format | Journal article |
| id | oxford-uuid:ee1091b2-5d37-4f1a-8149-aa6cd0f02cf6 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:06:37Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:ee1091b2-5d37-4f1a-8149-aa6cd0f02cf62022-03-27T11:29:54ZOn the average value of divisor sums in arithmetic progressionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ee1091b2-5d37-4f1a-8149-aa6cd0f02cf6Mathematical Institute - ePrints2005Heath-Brown, DBanks, WShparlinski, IWe consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that ``on average'' these sums are close to the expected value. We also give applications of our result to sums of the divisor function twisted with characters (both additive and multiplicative) taken on the values of various functions, such as rational and exponential functions; in particular, we obtain upper bounds for such twisted sums. |
| spellingShingle | Heath-Brown, D Banks, W Shparlinski, I On the average value of divisor sums in arithmetic progressions |
| title | On the average value of divisor sums in arithmetic progressions |
| title_full | On the average value of divisor sums in arithmetic progressions |
| title_fullStr | On the average value of divisor sums in arithmetic progressions |
| title_full_unstemmed | On the average value of divisor sums in arithmetic progressions |
| title_short | On the average value of divisor sums in arithmetic progressions |
| title_sort | on the average value of divisor sums in arithmetic progressions |
| work_keys_str_mv | AT heathbrownd ontheaveragevalueofdivisorsumsinarithmeticprogressions AT banksw ontheaveragevalueofdivisorsumsinarithmeticprogressions AT shparlinskii ontheaveragevalueofdivisorsumsinarithmeticprogressions |