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2155
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location Canada
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visits member for 3 years, 3 months
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I am a first year graduate student at Princeton university interested in Analytic Number Theory and Additive Combinatorics.

You can contact me at naslund [at] math [dot] princeton [dot] edu, or visit my website for more information.


2d
comment The sum over zeros in the explicit formula for $\zeta(s)$
I believe you mean $\psi(x)=\sum_{p^k<x} \log p$, rather than $\psi(x)=\sum_{p^k<x} \frac{\log p}{p^k}$.
Apr
6
accepted The intersection of $n$ cylinders in $3$-dimensional space
Mar
14
accepted A sumset inequality
Mar
13
comment A sumset inequality
@Alvin, Seva: I checked all possible combinations $X\subsetneq A\subset \{1,2,3\dots, 10\}$ and the inequality always holds. I edit the question to this in.
Mar
13
revised A sumset inequality
added 33 characters in body
Mar
13
revised A sumset inequality
added 708 characters in body
Mar
13
comment A sumset inequality
@Seva I wrote a program which chooses $A$ as a random subset of $\{1,2,...,n\}$ and $X$ as a random subset of $A$, and for $1$ million trials with $n=100$, the inequality always holds. I'll write a program that checks all subsets of $\{1,\dots,10\}$ and all possibilities $X$ and test it.
Mar
13
awarded  Nice Question
Mar
13
asked A sumset inequality
Feb
21
comment What is/are the best bound/s on the sum of squares of degrees in a graph?
A quick search yields the paper New sharp bounds on the first Zagreb index, where they show that for connected graphs $G=(V,E)$, $$M_1(G) \leq e(e+1)$$ $$M_1(G) \leq n(2n-e+1)$$which are each sharp for some graphs. Cauchy-Schwarz yields the lower bound $$4e^2/n\leq M_1(G).$$ We are essentially trying to bound the second moment of a function $d:V\rightarrow \mathbb{N}$ by the first moment and the size of the domain $V$, so any simple bounds will not be tight in every case.
Jan
16
awarded  Nice Question
Jan
13
awarded  Good Question
Jan
13
comment The intersection of $n$ cylinders in $3$-dimensional space
Thanks, this is what I was looking for.
Jan
13
comment The intersection of $n$ cylinders in $3$-dimensional space
In the link to the wikipedia page on Steinmetz solids, there is a nice gif: upload.wikimedia.org/wikipedia/commons/9/99/…
Jan
13
comment The intersection of $n$ cylinders in $3$-dimensional space
@WillSawin: Yes, I have added that in.
Jan
13
comment The intersection of $n$ cylinders in $3$-dimensional space
@JosephO'Rourke: The minimum volume is of interest since the maximum volume is infinite.
Jan
13
revised The intersection of $n$ cylinders in $3$-dimensional space
added 72 characters in body
Jan
13
asked The intersection of $n$ cylinders in $3$-dimensional space
Jan
12
awarded  Yearling
Dec
27
awarded  Announcer