Algebra & Number Theory Seminar
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Texas Tech University

Algebra & Number Theory Seminar

2017-2018

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Department of Mathematics & Statistics

Math 110

Wednesdays 3:00-4:00 pm

### Dermot McCarthy

Texas Tech University

#### Wednesday, 7 March, 2018

#### Math 110, 3:00 pm

**Title:** Sequences, Modular Forms and Cellular Integrals

**Abstract:** The Apéry numbers, which arise in the irrationality proofs for ζ(2) and ζ(3), satisfy many intriguing arithmetic properties, and are also related to the *p*-th Fourier coefficients of modular forms. We describe sequences associated to Brown's cellular integrals, of which the Apéry numbers are special cases. We discuss recent work on proving that the connection to modular forms persists for these sequences in general.