Home /  Combinatorics Seminar: The Taylor coefficients of the Jacobi theta constant θ3

Seminar

Combinatorics Seminar: The Taylor coefficients of the Jacobi theta constant θ3 October 08, 2018 (12:00 PM PDT - 01:00 PM PDT)
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Location: UC Berkeley Math (Evans Hall 939)
Speaker(s) Dan Romik (University of California, Davis)
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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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