276 reputation
22
bio website
location
age
visits member for 1 year, 6 months
seen Jun 24 '13 at 19:41

Apr
6
awarded  Yearling
May
31
awarded  Nice Answer
May
31
answered How does Yitang Zhang use Cauchy's inequality and Theorem 2 to obtain the error term coming from the $S_2$ sum
May
21
comment Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
After a first look at the paper, I actually have the impression that Zhang does not use automorphic results or techniques, but only some of the dispersion method / combinatorial ideas which occur as ingredients (together with automorphic results) in the works of Bombieri-Fouvry-Friedlander-Iwaniec...
May
21
comment Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
To be more precise, it is another estimate of Friedlander-Iwaniec (for the exponent of distribution of the $d_3$ divisor function) which depends on the estimate of Bombieri and Birch. This bound is indeed for a three-variable character sum, and requires square-root cancellation, so that there is certainly no known elementary proof (although it will probably be scrutinized rather carefully...)
May
21
comment How much of character theory can be done without Schur's lemma or the Artin-Wedderburn theorem?
Schur's Lemma is really old, I think. Burnside used it in 1905 almost with no justification, for instance... A completely off-hand suggestion: Deligne has defined a category that is supposed to behave like the representations of the symmetric group $S_t$ where $t$ is not a positive integer. Maybe those could be useful?
May
20
comment Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
Note: the first result of "Bombieri-Friedlander-Iwaniec style", going beyond the Riemann Hypothesis but not as far as the exponent $4/7$, is due to Fouvry-Iwaniec ("Primes in arithmetic progressions", Acta Arith. 42 (1983), 197-218; the exponent there is $9/17$). All these results depend crucially on the spectral theory of automorphic forms to estimates sum of Kloosterman sums, and especially on the results of Deshouillers and Iwaniec in this direction.
May
19
comment Good effective versions of theorems of Artin and Brauer
This is to some extent a question about lattices: there is the lattice of virtual representations of $G$, the basis of irreducible characters, the generating set of induced characters from cyclic subgroups, and the question is to minimize a certain complexity for expressing the basis vectors in terms of the other generating set. Maybe, once interpreted this way, there might be some information in the literature on lattices?
May
17
answered Good effective versions of theorems of Artin and Brauer
May
12
answered Applications and examples of quotient categories of abelian categories
May
6
awarded  Enthusiast
Apr
10
answered Jacobi sums on tori
Apr
6
awarded  Teacher
Apr
6
answered The $k^{th}$ derivative of a L-function has necessarily infinitely many zeros