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Nov
26 |
comment |
Proving a functional inequality
I wonder whether you typed the formula correctly. As it stands, $\left(n\atop m\right)$ can be pulled out of the sum. |
Nov
16 |
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Do names given to math concepts have a role in common mistakes by students?
And a hyperfinite von Neumann algebra can be properly infinite. |
Nov
11 |
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Why does the Gamma-function complete the Riemann Zeta function?
Actually, not quite. Define $\eta(z)=(1-2^{1-z})\zeta(z)=\sum_{n\ge 1}\frac{(-1)^{n+1}}{n^z}$. This sum converges (conditionally) when Re$\,z>0$, thus $\eta$ is defined in the same half-plane (modulo considerations for Re$\,z=1$. The functional equation for $\zeta$ leads to a functional equation for $\eta$. The latter makes sense without complex analysis since $\eta(s)$ and $\eta(1-s)$ are both defined if $0<s<1$. This functional equation was already published by Euler! See: 1) E. Landau: Euler und die Funktionalgleichung der Riemannschen Zetafunktion. 2) A. Weil: Prehistory of the zeta-func. |
Nov
11 |
comment |
What are some very important papers published in non-top journals?
I don't think that this is a reasonable example. The only reason why these papers have not been published properly is that Perelman didn't submit them anywhere. Annals or Acta would have accepted them. |
Oct
31 |
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Real-world applications of mathematics, by arxiv subject area?
Numerical mathematics, whose usefulness does not require proof, is just applied functional analysis. See for example Collatz' book "Functional analysis and numerical mathematics". By the way, this example nicely shows how futile the division between pure and applied math is. |
Nov
22 |
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Books you would like to read (if somebody would just write them…)
Quillen's algebraic K-theory for rings can be defined in terms of non-abelian homological algebra. The only book-length presentation that I know is this: Hvedri Inassaridze: Non-abelian homological algebra and its applications.Kluwer, 1997. ISBN: 0-7923-4718-8 It seems that this approach never got very popular. The book seems to be little known. |
Nov
18 |
answered | Applications of Brouwer's fixed point theorem |
Nov
18 |
answered | What is your favorite proof of Tychonoff's Theorem? |
Oct
12 |
answered | What is your favorite proof of Tychonoff's Theorem? |
Apr
1 |
awarded | Editor |
Apr
1 |
revised |
Is Higher K-functor the derived functor of K0?
edited body |
Apr
1 |
answered | Is Higher K-functor the derived functor of K0? |
Apr
1 |
awarded | Supporter |
Apr
6 |
answered | Prime Number Theorem w/o Complex Analysis |
Nov
18 |
comment |
Non-vanishing of zeta(s), Re(s)=1, without complex analysis?
Bost, Jean-Benoît |
Nov
18 |
answered | Non-vanishing of zeta(s), Re(s)=1, without complex analysis? |
Nov
17 |
awarded | Teacher |
Nov
17 |
answered | Non-vanishing of zeta(s), Re(s)=1, without complex analysis? |