bio | website | math.princeton.edu/directory/… |
---|---|---|
location | Princeton, New Jersey | |
age | 26 | |
visits | member for | 4 years, 7 months |
seen | 1 hour ago | |
stats | profile views | 2,042 |
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 |