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Congruence properties of the Taylor coefficients of the Jacobi theta constant \(\theta_3\)
Student-Run Research Seminar| Speaker: | Robert Scherer, UC Davis |
| Location: | 2112 MSB |
| Start time: | Tue, Apr 30 2019, 12:30PM |
Romik recently determined the Taylor expansion of the Jacobi theta constant \(\theta_3\), around the point \(x=1\). He discovered a new integer sequence, \(d(n)=1,1,-1,51,849,-26199,\ldots,\) from which the Taylor coefficients are built, and conjectured that the numbers \(d(n)\) satisfy certain congruences. We prove some of these conjectures.
There will be pizza.