bio | website | math.uwaterloo.ca/~y28xiao |
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location | Waterloo, ON | |
age | 28 | |
visits | member for | 4 years, 6 months |
seen | 3 hours ago | |
stats | profile views | 3,001 |
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.
May 24 |
awarded | Popular Question |
May 23 |
awarded | Proofreader |
May 23 |
reviewed | Edit Is the product of two supermodular functions supermodular? |
May 23 |
revised |
Is the product of two supermodular functions supermodular?
Improved formatting |
May 22 |
comment |
A not-so-weak Goldbach's conjecture
I think your 'definition' of 'natural' is too restrictive. The squares (which are the thickest of perfect powers) are too thin to apply the known arguments ins analytic number theory. It is possible that Helfgott's improvements can be applied to prove a 'weak Goldbach' for a set whose density is $O(x^\delta)$ with $\delta$ very close to one, but I doubt any such set would fit your definition of 'natural'. |
May 22 |
comment |
A not-so-weak Goldbach's conjecture
I am not sure if the question is well posed. It should be fairly easy to adapt Helfgott's arguments to apply to a subset of the primes say, defined by congruence conditions. Also, it is known that the number of exceptions to Goldbach's conjecture, up to $x$, is $O(x^\delta)$ for some positive $\delta < 1$, so it certainly is possible to adjoin a set of density $O(x^\delta)$ to remove the exceptions. |
May 22 |
revised |
A not-so-weak Goldbach's conjecture
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May 20 |
comment |
Numbers represented by inhomogeneous forms
I am not sure what kind of answer you are looking for. In general one cannot expect a simple description for the set of numbers represented by a specific function. Are you looking for things like whether a given polynomial represents all numbers? |
May 15 |
answered | Long gaps between primes |
May 7 |
revised |
Distribution of smooth values of polynomials
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May 7 |
asked | Distribution of smooth values of polynomials |
May 4 |
asked | Concentration of large prime factors of polynomials |
May 1 |
reviewed | Approve Is there an introduction to probability theory from a structuralist/categorical perspective? |
Apr 27 |
asked | Factoring a polynomial in a specific manner |
Apr 26 |
asked | Density of polynomials which are soluble with respect to a set of primes |
Apr 25 |
comment |
Density of polynomials with a prescribed number field extension
I modified the question to be more precise and non-trivial. |
Apr 25 |
revised |
Density of polynomials with a prescribed number field extension
added 111 characters in body |
Apr 25 |
asked | Density of polynomials with a prescribed number field extension |
Apr 23 |
reviewed | Reject Singular projective variety where the Cartan homomorphism is not an isomorphism? |
Apr 22 |
asked | When is it appropriate to name something a 'fundamental lemma'? |