Seminar
Parent Program: | -- |
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Location: | UC Berkeley Math (Evans Hall 939) |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
We study the Taylor expansion around the point x=1 of a classical modular form, the Jacobi theta constant θ3. This leads naturally to a new sequence (d(n))∞n=0=1,1,−1,51,849,−26199,… of integers, which arise as the Taylor coefficients in the expansion of a related "centered" version of θ3. We prove several results about the numbers d(n) and conjecture that they satisfy the congruence d(n)≡(−1)n−1 (mod 5) and other similar congruence relations.
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