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Jun
6
comment Existence of polynomials of degree $\geq 2$ which represent infinitely many prime numbers
@MicahMilinovich, how does one deduce that from Baier & Zhao's result? To the best of my knowledge, these results typically require that the number of polynomials in the family increase with other parameters in the average and thus do not imply asymptotic statements about any single (even a typical) polynomial. This is analogous to the fact that while Bombieri–Vinogradov is an averaged form of the RH, B-V does not imply that the RH holds even a single L-function.
May
30
awarded  Popular Question
Apr
6
revised Steinhaus's Easter Egg Problem
added 4 characters in body; edited tags
Apr
6
comment Steinhaus's Easter Egg Problem
Thank you, both. I'm a bit unclear on how exactly to make sense of the question as translated. Can anyone offer a clear interpretation of this?
Apr
5
awarded  Nice Question
Apr
5
asked Steinhaus's Easter Egg Problem
Mar
6
awarded  Revival
Feb
12
comment Primes and Parity
(cont) If one could do (and efficiently construct) this for a collection of APs of size, say, $n^{1/100}$ then it would solve the problem. It might be possible to probabilistically show the existence of such as collection. That wouldn't solve the problem on its own, but it would reduce the question to one of pseudo-randmness and not number theory. On the other hand, my intuition here isn't great and it might well be possible that such a collection can't exist.
Feb
12
comment Primes and Parity
Gil: yes, that is what I was thinking. I'd like to find a small collection of APs such that at least one is guaranteed to intersect any set (with certain properties which we can prove about the primes; size/density might be sufficient) in a set of odd parity...
Feb
10
comment Primes and Parity
A somewhat different question related to getting around the $\sqrt{n}$ barrier is the following: First recall that the Polymath4 result allows one to compute the parity of primes in an arithmetic progression intersecting [n,2n] "efficiently" (in time $n^{1/2-\delta}$ for some small $\delta$). Consider a subset $A \subseteq [n]$ of density $n/\log(n)$. What is the smallest collection of arithmetic progressions such that at least one is guaranteed to intersect $A$ with odd parity? More generally, it would be nice to reduce the problem to something not explicitly involving primes.
Jan
2
revised Connection between the Fourier transform of f and |f|
edited body
Jan
2
answered Connection between the Fourier transform of f and |f|
Nov
26
awarded  Enlightened
Nov
26
awarded  Nice Answer
Nov
26
awarded  Enlightened
Nov
26
awarded  Nice Answer
Nov
17
awarded  Good Question
Nov
13
awarded  Good Answer
Nov
7
answered A.e. pointwise convergence of L2 functions - counterexample for generalization of Carleson's thm
Oct
18
awarded  Yearling