DATE: Tuesday, March 16 (2010), at 12:50pm
PLACE: LIT 223
SPEAKER:
Alexander Berkovich
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TITLE:
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Sum of three squares and binary quadratic forms (Part 2)
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ABSTRACT:
George Andrews used Bailey's Lemma to prove the following
identity
Σ r(n) qn=
(Σ qn2)3
=
1+ 4 Σ qn/(1+ (-q)n) + ....
In this talk I will provide interpretation of this result in terms of
class numbers of binary quadratic forms.
I will explain how to use this interpretation to prove that
r(n)= 0 iff n= 4a (8b+ 7) for some natural numbers a,b.
If time permits, I will discuss some explicit ( and hopefully correct)
formulas such as
r(n) = -(24/n) Σ m jacobi(-n|m)
with n being square free integer congruent to 3 mod 8.
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