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39m
accepted Etale cohomology approach on $\tau(n)$
6h
comment Are there any Algebraic Geometry Theorems that was proved using Combinatorics?
As I heard everything is about counting stated abstractly.
15h
comment Etale cohomology approach on $\tau(n)$
"Qiaochu Yuan says Consider also the following heuristic argument. The pentagonal number theorem in fact lets us write $τ(n−1)$ as a sum of $O(n^{12})$ signs. Assume that these signs are randomly distributed. Then one expects their sum to have absolute value $O(n^6)$ by a straightforward variance calculation. This is the same sort of argument that correctly suggests that Gauss sums should have absolute value around $\sqrt{p}$. But in fact Ramanujan's conjecture is better than this by a factor of $\sqrt{n}$. I don't know where this extra savings comes from even heuristically."
15h
comment Etale cohomology approach on $\tau(n)$
So this is not case of mysterious cancellations improving on random averaging argumentation?
21h
comment Etale cohomology approach on $\tau(n)$
"Langlands observed that knowledge of the poles of symmetric power L-functions attached to Δ would be sufficient to conclude that |τ(p)|≤2p11/2, and Deligne observed that there was a nice translation of this idea into Grothendieck's cohomology theory" Is there a way to make this more explicit?
1d
asked Etale cohomology approach on $\tau(n)$
Mar
23
comment Factorization of antiderivative of minimal polynomials
@rickkenyon motivation?
Mar
23
comment On ranks of matrix products
so you are considering a block diagonal matrix? ok.
Mar
23
comment On ranks of matrix products
sorry what is $\oplus$ here? directsummation?
Mar
23
asked On ranks of matrix products
Mar
23
comment addition chains for products of relatively prime factors
Suitable on cstheory perhaps?
Mar
23
comment A convex analysis theorem improvement
Could you also elaborate to an answer?
Mar
23
comment A convex analysis theorem improvement
@BillJohnson Could you please refer the paper by D.R. Lewis?
Mar
21
comment A convex analysis theorem improvement
@BillJohnson Thank you. Any situations we could hope to improve?
Mar
21
asked A convex analysis theorem improvement
Mar
21
revised A question in Banach space
deleted 200 characters in body
Mar
20
revised A question in Banach space
added 98 characters in body
Mar
20
revised A question in Banach space
added 54 characters in body
Mar
20
asked A question in Banach space
Mar
18
comment Another formulation of error-correcting coding problem
could you provide details on capacity calculation?