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Nov
17
comment stationary phase method in analytic number theory
The method of stationary phase is covered in many standard books: e.g. De Bruijn's Asymptotic methods in analysis; Titchmarsh's Theory of the Riemann zeta function; Stein's books on harmonic analysis; Montgomery's 10 lectures on harmonic analysis and analytic number theory; Graham and Kolesnik's book on exponential sums ... . I hope you can find one of these books in your library.
Nov
17
answered Mobius function of consecutive numbers
Nov
17
reviewed No Action Needed What motivated Rademacher's contour along the Ford circles?
Nov
16
comment Questions on de Branges' work on the Riemann hypothesis
As Alex R and Dan Petersen have pointed out there is some information on this already on MO, and on Wikipedia. One could also look at this paper by Lagarias: math.lsa.umich.edu/~lagarias/doc/debranges-houches.pdf .
Nov
16
reviewed Leave Closed Determining the position of a coordinate by binning Gaussian noise around that coordinate to lattice points with vertex-specific probabilities
Nov
16
reviewed Leave Closed When did you “meet Polya”?
Nov
16
reviewed Leave Closed Questions on de Branges' work on the Riemann hypothesis
Nov
14
comment Bounds on the largest root of a polynomial
@PietroMajer: Note that $f(k)$ is negative. So starting Newton approximations from $k$ gives exactly what the problem wants.
Nov
14
awarded  Custodian
Nov
14
reviewed No Action Needed Bounds on the largest root of a polynomial
Nov
14
comment Bounds on the largest root of a polynomial
Eventually the polynomial is positive. If you plug in a value given by a Newton approximation and find a negative value then the root lies above it. I think your polynomial is simple enough that this will work without too much trouble.
Nov
14
comment Bounds on the largest root of a polynomial
Newton's method starting near $k$ should be good enough?
Nov
13
awarded  Custodian
Nov
13
reviewed No Action Needed About Kodaira's book on deformations
Nov
13
reviewed Looks OK Given an exact category, viewed as a site, do there exist non-additive sheaves?
Nov
13
revised For which $n$ is there only one group of order $n$?
added 268 characters in body
Nov
13
answered For which $n$ is there only one group of order $n$?
Nov
13
comment For which $n$ is there only one group of order $n$?
Presumably the density of $n$ with $f(n)=1$ is zero, because there are lots of semidirect products.
Nov
12
comment Coloring $K_n$ via edge-weight sums
@JosephO'Rourke: Thanks for the plot! The plot seems correct (or at least I'm happy since it matches my conjecture!), but there's a little typo in the formula just above the graph -- the numerator in the exponent should be $n^{3/2}$ and the denominator $k$. Thanks again for the nice graph (and question!).
Nov
12
comment Coloring $K_n$ via edge-weight sums
@JosephO'Rourke: Just for clarity: when $n=5$ (coloring $K_5$) and $k=10$ from your plot the answer seems to be about $0.6$. My conjecture gives $\exp(-\sqrt{3} 5^{1.5}/(20\sqrt{\pi}))$ which is about $0.58$.