Moments of zeta and correlations of divisor-sums: V
In this series of papers we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper completes the general study of what we call Type II sums which utilize a circle me...
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| Format: | Journal article |
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London Mathematical Society
2018
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| _version_ | 1797077730841329664 |
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| author | Conrey, B Keating, J |
| author_facet | Conrey, B Keating, J |
| author_sort | Conrey, B |
| collection | OXFORD |
| description | In this series of papers we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper completes the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asymptotic formula for the mean square along [T, 2T] of a Dirichlet polynomial of arbitrary length with divisor functions as coefficients. |
| first_indexed | 2024-03-07T00:22:10Z |
| format | Journal article |
| id | oxford-uuid:7cede4b8-4d0b-4ef5-b300-3d12d459277c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:22:10Z |
| publishDate | 2018 |
| publisher | London Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:7cede4b8-4d0b-4ef5-b300-3d12d459277c2022-03-26T21:00:03ZMoments of zeta and correlations of divisor-sums: VJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7cede4b8-4d0b-4ef5-b300-3d12d459277cSymplectic Elements at OxfordLondon Mathematical Society2018Conrey, BKeating, JIn this series of papers we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper completes the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asymptotic formula for the mean square along [T, 2T] of a Dirichlet polynomial of arbitrary length with divisor functions as coefficients. |
| spellingShingle | Conrey, B Keating, J Moments of zeta and correlations of divisor-sums: V |
| title | Moments of zeta and correlations of divisor-sums: V |
| title_full | Moments of zeta and correlations of divisor-sums: V |
| title_fullStr | Moments of zeta and correlations of divisor-sums: V |
| title_full_unstemmed | Moments of zeta and correlations of divisor-sums: V |
| title_short | Moments of zeta and correlations of divisor-sums: V |
| title_sort | moments of zeta and correlations of divisor sums v |
| work_keys_str_mv | AT conreyb momentsofzetaandcorrelationsofdivisorsumsv AT keatingj momentsofzetaandcorrelationsofdivisorsumsv |