DATE: Tuesday, September 22 (2009), at 3:00pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
Ramanujan's proof of Bertrand's postulate
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ABSTRACT:
Bertrand conjectured and Chebychev proved that
for x > 1, there is always a prime between x and 2x. Ramanujan
gave a beautiful proof of Bertrand's postulate which is simpler
than Chebychev's. The key idea in Ramanujan's proof of
Bertrand's postulate is similar to the the trick he (Ramanujan)
used to "prove" his outrageous claim
1+2+3+... = -1/12.
This crazy identity is actually true if we interpret the left hand
side as formally representing the Riemann zeta function at -1.
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