Difference between revisions of "NTS ABSTRACTFall2019"
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | ||
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− | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | ''' | + | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Sawin''' |
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− | | bgcolor="#BCD2EE" align="center" | | + | | bgcolor="#BCD2EE" align="center" | The sup-norm problem for automorphic forms over function fields and geometry |
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− | | bgcolor="#BCD2EE" | We | + | | bgcolor="#BCD2EE" | |
+ | The sup-norm problem is a purely analytic question about | ||
+ | automorphic forms, which asks for bounds on their largest value (when | ||
+ | viewed as a function on a modular curve or similar space). We describe | ||
+ | a new approach to this problem in the function field setting, which we | ||
+ | carry through to provide new bounds for forms in GL_2 stronger than | ||
+ | what can be proved for the analogous question about classical modular | ||
+ | forms. This approach proceeds by viewing the automorphic form as a | ||
+ | geometric object, following Drinfeld. It should be possible to prove | ||
+ | bounds in greater generality by this approach in the future. | ||
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Revision as of 14:47, 19 August 2019
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Sep 5
Will Sawin |
The sup-norm problem for automorphic forms over function fields and geometry |
The sup-norm problem is a purely analytic question about automorphic forms, which asks for bounds on their largest value (when viewed as a function on a modular curve or similar space). We describe a new approach to this problem in the function field setting, which we carry through to provide new bounds for forms in GL_2 stronger than what can be proved for the analogous question about classical modular forms. This approach proceeds by viewing the automorphic form as a geometric object, following Drinfeld. It should be possible to prove bounds in greater generality by this approach in the future. |