[math-fun] Oops. Universe not what they said.
http://arxiv.org/abs/1408.1706 http://iopscience.iop.org/0004-637X/803/1/20/ Peter A. Milne, Ryan J. Foley, Peter J. Brown, and Gautham Narayan: The Changing Fractions of Type Ia Supernova NUV--Optical Subclasses with Redshift, The Astrophysical Journal 803,1 (2015) 20- The "type IA supernova standard candles" that were used to win Nobel pries, prove the universe is accelerating expansion, due to (apparently) Einstein cosmical constant "Lambda," etc, etc... ...aren't. That is, UV observations now show there really are two classes of these candles, which erroneously were lumped into one basket -- and more seriously, one class predominates nearer to us, the other, further. Hence, all that work is now called into question and presumably needs to be entirely redone, and the probable conclusion will be that there is a lot less Lambda than they thought. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
"What we’ve learned from this is that the amount of dark energy and the typeof dark energy we infer from supernovae may change slightly and in a subtle manner, and this may actually be good for bringing the three methods — supernovae, the CMB and BAO — into better alignment. This is one of those great moments in science where one incorrect assumption doesn’t cause us to throw all our results and conclusions out, but rather where it helps us more accurately understand a phenomenon that’s puzzled us since we first discovered it." https://medium.com/starts-with-a-bang/ask-ethan-83-what-if-dark-energy-isn-t... On Sat, Apr 11, 2015 at 6:53 PM, Warren D Smith <warren.wds@gmail.com> wrote:
http://arxiv.org/abs/1408.1706 http://iopscience.iop.org/0004-637X/803/1/20/ Peter A. Milne, Ryan J. Foley, Peter J. Brown, and Gautham Narayan: The Changing Fractions of Type Ia Supernova NUV--Optical Subclasses with Redshift, The Astrophysical Journal 803,1 (2015) 20-
The "type IA supernova standard candles" that were used to win Nobel pries, prove the universe is accelerating expansion, due to (apparently) Einstein cosmical constant "Lambda," etc, etc...
...aren't. That is, UV observations now show there really are two classes of these candles, which erroneously were lumped into one basket -- and more seriously, one class predominates nearer to us, the other, further.
Hence, all that work is now called into question and presumably needs to be entirely redone, and the probable conclusion will be that there is a lot less Lambda than they thought.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
What's now called Riemann's xi function is (up to a constant factor): xi(s) := s(s-1) zeta(s) gamma(s/2) pi^(-s/2), which is an entire function of s, and its zeroes (the values of s for which xi(s) = 0) are exactly the mysterious "nontrivial" zeroes of zeta(s). Another function (that Riemann called "xi(t)") is now usually called Landau's capital-xi(t) function: Ξ(t). But since Ξ may not appear correctly in your e-mail, I'll call it X(t): X(t) := xi(1/2 + i t). It's easy to check that X(t) is real on the real axis and satisfies X(t) == X(-t), which is equivalent to the "functional equation of zeta". I would like to know the power series coefficients of X(t) about 0. Mathematica's attempt to do this results in unbelievably complicated expressions, and I've had very little luck simplifying them. Wikipedia gives an expression for this power series — but each coefficient is expressed as an infinite series in terms of the mysterious nontrivial zeroes of the zeta function. QUESTION (mostly to you-know-who): Is there a more or less straightforward expression for the power series coefficients of X(t) ??? (Of course, since X(t) == X(-t), only the even powers of t have nonzero coefficients.) --Dan
participants (3)
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Dan Asimov -
Mike Stay -
Warren D Smith