An $L^4$ maximal estimate for quadratic Weyl sums
We show that $$\bigg\|\sup_{0 < t < 1} \big|\sum_{n=1}^{N} e^{2\pi i (n(\cdot) + n^2 t)}\big| \bigg\|_{L^{4}([0,1])} \leq C_{\epsilon} N^{3/4 + \epsilon}$$ and discuss some applications to the theory of large values of Weyl sums. This estimate is sharp for quadratic Weyl sums, up to the loss o...
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| creator | Barron, Alex |
| description | We show that $$\bigg\|\sup_{0 < t < 1} \big|\sum_{n=1}^{N} e^{2\pi i
(n(\cdot) + n^2 t)}\big| \bigg\|_{L^{4}([0,1])} \leq C_{\epsilon} N^{3/4 +
\epsilon}$$ and discuss some applications to the theory of large values of Weyl
sums. This estimate is sharp for quadratic Weyl sums, up to the loss of
$N^{\epsilon}$. |
| doi_str_mv | 10.48550/arxiv.2011.09885 |
| format | Article |
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(n(\cdot) + n^2 t)}\big| \bigg\|_{L^{4}([0,1])} \leq C_{\epsilon} N^{3/4 +
\epsilon}$$ and discuss some applications to the theory of large values of Weyl
sums. This estimate is sharp for quadratic Weyl sums, up to the loss of
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(n(\cdot) + n^2 t)}\big| \bigg\|_{L^{4}([0,1])} \leq C_{\epsilon} N^{3/4 +
\epsilon}$$ and discuss some applications to the theory of large values of Weyl
sums. This estimate is sharp for quadratic Weyl sums, up to the loss of
$N^{\epsilon}$.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Classical Analysis and ODEs</subject><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrtuwjAUgGEvDAj6AEz1kDXp8S3YY4RoQYrEEomt0XFsS5ESLk5A8PalwPRvvz5CFgwyqZWCL4y39ppxYCwDo7WaElYcaFL-yoT2eGt77KgfxkdHT8Mx0vMFXcSxbeje3zs6XPphTiYBu8F_vDsj1fe6Wm3ScvezXRVlivlSpbkEkBqsyVEYgU0I3DKOzlnHuXJMS5E7xhV4a7ldgmyMDsYjR7TKGy9m5PO1fZrrU3yg4r3-t9dPu_gDwfg9ng</recordid><startdate>20201119</startdate><enddate>20201119</enddate><creator>Barron, Alex</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20201119</creationdate><title>An $L^4$ maximal estimate for quadratic Weyl sums</title><author>Barron, Alex</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-6400480b96a393acff2b12addbd225d18436d1250ebb2b704c98f9ea2aab5e9e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Classical Analysis and ODEs</topic><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Barron, Alex</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Barron, Alex</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An $L^4$ maximal estimate for quadratic Weyl sums</atitle><date>2020-11-19</date><risdate>2020</risdate><abstract>We show that $$\bigg\|\sup_{0 < t < 1} \big|\sum_{n=1}^{N} e^{2\pi i
(n(\cdot) + n^2 t)}\big| \bigg\|_{L^{4}([0,1])} \leq C_{\epsilon} N^{3/4 +
\epsilon}$$ and discuss some applications to the theory of large values of Weyl
sums. This estimate is sharp for quadratic Weyl sums, up to the loss of
$N^{\epsilon}$.</abstract><doi>10.48550/arxiv.2011.09885</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs Mathematics - Number Theory |
| title | An $L^4$ maximal estimate for quadratic Weyl sums |
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