3,760 reputation
31247
bio website math.uwaterloo.ca/~y28xiao
location Waterloo, ON
age 28
visits member for 4 years, 8 months
seen 1 hour ago

PHD Candidate in Pure Mathematics, University of Waterloo. I am being advised by Professor Cameron Stewart, FRSC.

I am interested in analytic number theory, prime number theory, transcendence theory, and power-free values of polynomials. In particular I work on problems involving applications and generalizations of the determinant methods pioneered by Bombieri/Pila, Heath-Brown, and Salberger, including the real analytic determinant method, the approximate determinant method of Heath-Brown, and the global determinant method of Salberger (an extension of the $p$-adic determinant method of Heath-Brown), as well as other potential variants.


3h
reviewed Approve Counting subspaces
7h
comment Counting function for prime pair with bounded gaps between them
@LironYedidsion The answer given in your link is not what you're looking for I don't think. Zhang's proof can be strengthened (as can all such similar results) to obtain an asymptotic lower bound for the number of prime pairs that are say at most 70 million apart. This bound is of course at most $x$, since $x$ is the length of the interval. What you are looking for is a polynomial bound for the parameter $h(m)$ which guarantees that there are infinitely many $m$-tuples of primes which are $h(m)$ apart, which is not at all the same thing.
1d
revised Counting function for prime pair with bounded gaps between them
edited body
1d
answered Counting function for prime pair with bounded gaps between them
Jul
25
reviewed Approve How do I convert a uniform value in [0,1) to a standard normal (Gaussian) distribution value?
Jul
20
comment Intersection of two lattices
Thank you for your response, this is exactly what I was looking for!
Jul
20
accepted Intersection of two lattices
Jul
20
asked Intersection of two lattices
Jul
20
reviewed Approve Can a continuous surjection from a Hilbert cube to a segment behave bad wrt Lebesgue measures?
Jul
18
reviewed Approve formal group laws of Abelian varieties in positive characteristic
Jul
18
accepted Cases where the number field case and the function field (with positive characteristic) are different
Jul
18
comment Cases where the number field case and the function field (with positive characteristic) are different
Very thorough, thank you for your insights!
Jul
18
comment Cases where the number field case and the function field (with positive characteristic) are different
This answer is fantastic! I recently taught elementary number theory and included the Miller-Rabin result. This is a marvelously simple demonstration of the difference!
Jul
18
awarded  Nice Question
Jul
17
reviewed Approve Is the set of the convolutions of two-point measures dense in the set of all measures?
Jul
16
reviewed Reject Linear vs smooth actions of finite groups on spheres, euclidean spaces and closed disks
Jul
15
reviewed Approve “Spec” of graded rings?
Jul
15
accepted Representations of the unit group in a ring of integers
Jul
15
awarded  Enlightened
Jul
15
awarded  Nice Answer