DATE: Tuesday, February 9 (2010), at 12:50pm
PLACE: LIT 305
SPEAKER: Alexander Berkovich
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TITLE:
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Ramanujan's 1Ψ1 summation and some Lambert series identities
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ABSTRACT:
Then I will show how to employ
Ramanujan's 1Ψ1 summation
to prove that
ΣΣ q(n2+ m2) =
1+4 Σ ( jacobi(-4|n ) qn/ (1-qn)
and
ΣΣ (q(n2+ nm+ m2) =
1+6 Σ ( jacobi(-3|n ) qn/ (1-qn)
where |q|<1.
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