Sum-product estimates and finite point configurations over p-adic fields
<p>We examine Erd\"{o}s-Falconer type problems in the setting of $p$-adic numbers, and establish bounds on the size of a set $E$ in $\Q_p</p><p>d$ that will guarantee $E\cdot E+E\cdot E+\ldots+E\cdot E$ has positive Haar measure. Under a mild regularity assumption, we establis...
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University of Rochester
2017
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ndltd-PROQUEST-oai-pqdtoai.proquest.com-102370202017-01-12T16:06:01Z Sum-product estimates and finite point configurations over p-adic fields Ethier, Dillon Mathematics <p>We examine Erd\"{o}s-Falconer type problems in the setting of $p$-adic numbers, and establish bounds on the size of a set $E$ in $\Q_p</p><p>d$ that will guarantee $E\cdot E+E\cdot E+\ldots+E\cdot E$ has positive Haar measure. Under a mild regularity assumption, we establish a lower bound on the dimension of a set that determines a set of simplices of positive measure, which reduces to an analogue of the distance problem when $1$-simplices are considered. Using the Mattila integral, we establish a different bound that improves upon the first bound when the dimension of the simplices is close to the ambient dimension. University of Rochester 2017-01-06 00:00:00.0 thesis http://pqdtopen.proquest.com/#viewpdf?dispub=10237020 EN |
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NDLTD |
| language |
EN |
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NDLTD |
| topic |
Mathematics |
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Mathematics Ethier, Dillon Sum-product estimates and finite point configurations over p-adic fields |
| description |
<p>We examine Erd\"{o}s-Falconer type problems in the setting of $p$-adic numbers, and establish bounds on the size of a set $E$ in $\Q_p</p><p>d$ that will guarantee $E\cdot E+E\cdot E+\ldots+E\cdot E$ has positive Haar measure. Under a mild regularity assumption, we establish a lower bound on the dimension of a set that determines a set of simplices of positive measure, which reduces to an analogue of the distance problem when $1$-simplices are considered. Using the Mattila integral, we establish a different bound that improves upon the first bound when the dimension of the simplices is close to the ambient dimension. |
| author |
Ethier, Dillon |
| author_facet |
Ethier, Dillon |
| author_sort |
Ethier, Dillon |
| title |
Sum-product estimates and finite point configurations over p-adic fields |
| title_short |
Sum-product estimates and finite point configurations over p-adic fields |
| title_full |
Sum-product estimates and finite point configurations over p-adic fields |
| title_fullStr |
Sum-product estimates and finite point configurations over p-adic fields |
| title_full_unstemmed |
Sum-product estimates and finite point configurations over p-adic fields |
| title_sort |
sum-product estimates and finite point configurations over p-adic fields |
| publisher |
University of Rochester |
| publishDate |
2017 |
| url |
http://pqdtopen.proquest.com/#viewpdf?dispub=10237020 |
| work_keys_str_mv |
AT ethierdillon sumproductestimatesandfinitepointconfigurationsoverpadicfields |
| _version_ |
1718407457745666048 |