2,246 reputation
11424
bio website math.princeton.edu/directory/…
location Princeton, New Jersey
age 26
visits member for 4 years, 7 months
seen 1 hour ago

PhD student at Princeton University


Sep
11
reviewed Approve suggested edit on “Counter”-example for Gauss's Lemma on irreducible polynomials
Sep
5
reviewed Edit suggested edit on Totally Geodesic Submanifolds
Sep
5
revised Totally Geodesic Submanifolds
Fixed broken MathJaX (otherwise unreadable)
Sep
5
comment Laplacian eigenfunction $L^p$ norms
Search for Sogge's results on $L^p$ bounds. I believe this is an active area of study, especially when one restricts to manifolds with interesting geometric properties.
Aug
22
reviewed Approve suggested edit on A lifting problem
Aug
22
reviewed Approve suggested edit on Operator norm vs spectral radius for positive matrices
Aug
14
comment Smallest prime in an arithmetic progression
If one assumes GRH, then one can obtain much stronger results: see, e.g. Corollary 1.2 of arxiv.org/abs/1309.3595, which shows the strict bound $(\phi(b) \log b)^2$.
Aug
14
revised lower and upper bound for $\sum_{k=1}^n \frac{(-1)^{\Omega(k)}}k$?
fixed grammar, changed tags
Aug
13
reviewed Approve suggested edit on Matching number and chromatic number
Aug
13
awarded  Enlightened
Aug
12
awarded  Nice Answer
Aug
12
answered lower and upper bound for $\sum_{k=1}^n \frac{(-1)^{\Omega(k)}}k$?
Aug
10
comment Inverse problem for zeta functions of curves over finite fields
This is a duplicate of a question I asked here: mathoverflow.net/questions/70605/from-zeta-functions-to-curves.
Aug
5
comment The shortest interval for which the prime number theorem holds
@SylvainJULIEN, this only makes sense in the function field setting, where zeta functions correspond to polynomials. But even there one expects that the linear independence hypothesis holds for every smooth ordinary curve over a finite field with absolutely simple Jacobian (this is a conjecture of Ahmadi and Shparlinski), and almost every curve is of this form.
Aug
5
comment The shortest interval for which the prime number theorem holds
@SylvainJULIEN, so while we do expect that a single zero determines an L-function in the sense that any given point on the critical line should be the zero of at most one primitive L-function, I see no reason why one should conclude from this that nontrivial zeroes of a fixed L-function may depend on each other in some way.
Aug
5
comment The shortest interval for which the prime number theorem holds
@SylvainJULIEN, we of course believe that no two primitive L-functions share a common nontrivial zero; in fact, a strong form of the linear independence hypothesis states that the set of all nontrivial zeroes of any finite collection of primitive L-functions is linearly independent over the rationals.
Aug
5
comment The shortest interval for which the prime number theorem holds
@SylvainJULIEN, that conjecture is almost certainly false, as follows from the linear independence hypothesis. See Nathan Ng's work on the limiting logarithmic distribution of the summatory function of the Möbius function.
Aug
5
comment The shortest interval for which the prime number theorem holds
@EmilJeřábek, Sound's paper is here: link.springer.com/chapter/10.1007/978-1-4020-5404-4_4. Page 79 there is pages 17 and 18 of the arXiv version.
Aug
4
reviewed Approve suggested edit on Why are they called Specht Modules?
Aug
2
reviewed Approve suggested edit on Existence of solutions of a polynomial system