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Aug
23
comment Is the functional equation for $\zeta (s) \left(1-\frac{1}{3^{s-1}}\right)$ known?
Yes, just change $2^{-s}$ to $3^{-s}$ (and $2^{-s-1}$ to $3^{-s-1}$) in the func. equations for $\eta$.
Aug
21
comment The form of the zeta function of an elliptic curve over a finite field
And of course a proof for $y^2=x^3-x$ goes back to Gauss (see e.g. Ireland, Rosen. A Classical Introduction to Modern Number Theory, ch. 8 for the proof)
Aug
21
comment The form of the zeta function of an elliptic curve over a finite field
Well, there is a relatively elementary proof in Silverman. The Arithmetic of Elliptic Curves
Aug
10
comment Cohomology of $K(\mathbb{Z}_2, n)$
See doc.rero.ch/record/482/files/Clement_these.pdf (including tables in Appendix C). In particular, yes, $H^5(K(Z/2,2))$ has 4-torsion, and no, I don't think there is a really simple and explicit answer.
Aug
9
comment A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta)
related: math.stackexchange.com/q/1284161
Aug
9
comment A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta)
the link is dead...
Jul
1
comment Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?
@Assad that proof is indeed simple — but gives a proof only of a much weaker statement, AFAICS (only about dim=3)
Jun
27
comment Is this problem correct?
also a duplicate of math.stackexchange.com/q/25701
Jun
27
comment Show that $ \sum_{r=1}^{n-1}\binom{n-2}{r-1}r^{r-1}(n-r)^{n-r-2}= n^{n-2} $
That's called Abel[-Hurwitz] identity, I believe.
Jun
24
comment Strehl identity for the sum of cubes of binomial coefficients
Nice. Since you don't really use change of variables etc one can get rid of all integrals and get a slightly shorter version in the language of gen. functions.
Jun
24
comment Strehl identity for the sum of cubes of binomial coefficients
Thank you, I'll take a look
Jun
23
comment Where to find Yuri Manin's “Lectures on zeta functions and motives”
mpim-bonn.mpg.de/preblob/4793
Jun
20
comment Recurrence $(n+2)\text{Cat}_{n+1}=(4n+2)\text{Cat}_n$ for non-crossing matchings
Understanding is its own reward.
Jun
17
comment Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
See also an example of using Jacobi sums to count points on $y^2=x^3-x$.
Jun
15
comment Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
1) «Rational parametrization of conics»; 2) «Jacobi sums».
Jun
15
comment $SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong \mathbb A_4$
From geometric POV the homomorphism to $A_4$ comes from the action of $SL_2(\mathbb Z_3)$ on 4-element set $P^1(\mathbb Z_3)$ (by fractional-linear transformations, if you will). Cf. $PSL_2(\mathbb F_4)\cong A_5$ etc.
Jun
7
comment Proof of $\sum_{n=1}^\infty \frac{1}{n^4 \binom{2n}{n}}=\frac{17\pi^4}{3240}$
related: math.stackexchange.com/q/144985
Jun
4
comment Why universal G-bundles are contractible?
If $B$ represents the functor «$X$ → principal $G$-bundles on $X$», then $E$ represents the functor «$X$ → principal $G$-bundles on $X$ with a fixed section». This functor is trivial, so $E$ is contractible.
May
14
comment Expected number of returns by time n in a symmetric 1-d random walk?
possible duplicate of Expected number of returns to zero in a symmetric random walk - closed form
May
13
comment Proving that $SL_2(\mathbb{Z}_5) / \{\pm I\}\simeq A_5$
cf. math.stackexchange.com/q/93762/152