# NTS ABSTRACTFall2019: Difference between revisions

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and geometry | 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. | |||

|} | |} |

## Revision as of 19:37, 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. |