bio | website | math.ucla.edu/~mlewko |
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location | ||
age | ||
visits | member for | 5 years, 5 months |
seen | 54 mins ago | |
stats | profile views | 4,007 |
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 |
Oct 13 |
answered | $L^2$ boundedness of the Hilbert transform via Cotlar-Stein Lemma |
Jul 6 |
answered | Proof of the Friedlanderâ€“Iwaniec theorem |
Jul 2 |
awarded | Curious |
May 5 |
comment |
Distribution of $a^2+\alpha b^2$
This isn't an answer, but there is a theorem of Atkin which is in a similar spirit: These exists a sequence of integers such that the n-th term is $n^2 + O(log(n))$ and whose sumset has positive density in the integers. ams.org/mathscinet-getitem?mr=202687 |
Apr 29 |
answered | A question on Cramer's theorem |
Apr 9 |
comment |
Fourier series of functions on compact groups
@Anton, If you interpret the question like that it isn't very interesting. There are certainly $L^2$ functions on the circle without absolutely convergent Fourier series. You could alternately ask for unconditional pointwise convergence (that is a.e. pointwise convergence for every ordering) but this is false for every complete infinite orthonormal system (such as Fourier series on the cirlce, again). |