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visits | member for | 1 year, 4 months |
seen | 2 hours ago | |
stats | profile views | 6,237 |
Nov 17 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 $0.58$. |