Difference between revisions of "NTS ABSTRACTFall2019"

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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Euclid'''
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Will Sawin'''
 
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| bgcolor="#BCD2EE"  align="center" | Infinitely many primes
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| bgcolor="#BCD2EE"  align="center" | The sup-norm problem for automorphic forms over function fields and geometry
 
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| bgcolor="#BCD2EE"  | We introduce the notion of a prime number, and show that there are infinitely many of those.
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| bgcolor="#BCD2EE"  |  
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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.