# Eric Naslund

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## Registered User

 Name Eric Naslund Member for 2 years Seen 21 hours ago Website Location Vancouver Age
My interests lean towards Analytic Number Theory and Additive Combinatorics.

You can contact me at: naslund (at) princeton.edu

 Apr18 comment Estimates for the size of the product set [n].[n]This is an exact duplicate of: mathoverflow.net/questions/108912/… Mar25 answered Recovering $\sum_{n \leq x} a(n)$ from $\sum_{n \leq x} a(n)e^{-n/x}$ Mar19 comment Probability that two random integers are coprimeSee the last part of this Math Stack Exchange answer: math.stackexchange.com/a/38142/6075 Mar18 comment Is there an explicit expression for the imaginary part of some non-trivial zero of zeta,At at a colloquium I once heard the comment, "Can we even prove that all the zeros of every primitive L-function are not all rational multiples of each other?" Mar12 awarded ● Popular Question Mar12 revised Integer Points on the Elliptic Curve $y^2=x^3+17$.deleted 243 characters in body; edited title Mar12 revised Mathematical Advice for Interested Highschool Studentsdeleted 61 characters in body Mar1 awarded ● Popular Question Mar1 comment Euler constant transcendality.The question of irrationality is still open. See: en.wikipedia.org/wiki/… Mar1 comment How to rewrite this totient summation in terms of Mertens?@Will Jagy: I didn't see the question on Math Stack Exchange until after answering this. Mar1 comment How to rewrite this totient summation in terms of Mertens?When $l=0$ you obtain the result at the displayed equation in my answer above. Mar1 accepted How to rewrite this totient summation in terms of Mertens? Mar1 answered How to rewrite this totient summation in terms of Mertens? Feb19 comment Prime race in 2 dimensions@Stefan: I don't think you are normalizing correctly. Looking at the count of primes up to $3.206\cdot 10^{11}$, we expect the error term in the prime number race to be around $\sqrt{x}/\log x$, or in your case $$\sqrt{3.206*10^{11}}/\log(3.206*10^{11})\approx 21371.$$ Feb3 accepted A curious limit involving prime numbers and composite numbers Feb1 comment Prime race in 2 dimensions@Teo B: The movement in the negative and positive direction comes from the prime number race modulo $8$ between the residues $1$ and $5$. More often than not, there will be more primes congruent to $5$ modulo $8$ than $1$. (To be specific, we need to talk about the logarithmic density and assume GRH and LI) The first time that the primes congruent to $1$ modulo $8$ pulls ahead in the race is between $10^8$ and $10^9$. Feb1 comment Should I tell my coauthor?This may be more appropriate on academia.stackexchange.com Jan20 comment Probability of all combinations of k numbers among n being coprimeHow are the $x_1,\dots,x_n$ chosen? If they are all multiples of two, then the gcd condition never happens. Jan12 awarded ● Yearling Jan3 comment A closed form of infinite products of complex zeros involving $\Im(\rho_n)$. Does a proof of this closed form imply RH? @Andy Putman: I don't think the OP claimed to have proved RH. His question is whether a particular statement is equivalent to RH. Dec31 comment 3-7 primes in base 10Can we even prove that there are infinitely many primes which in their decimal expansion do not contain the digit $9$? Dec25 revised Using Quotient of Prime Numbers to Approximation Realsadded 166 characters in body; added 57 characters in body; deleted 6 characters in body Dec25 comment Using Quotient of Prime Numbers to Approximation Reals@quid: Thank you for your comments. I found the [paper](arxiv.org/abs/math/0609615), it is also by Goldston, Graham, Pintz and Yıldırım. Dec25 revised Using Quotient of Prime Numbers to Approximation Realsadded 1 characters in body Dec25 awarded ● Enlightened Dec25 awarded ● Nice Answer Dec25 accepted Using Quotient of Prime Numbers to Approximation Reals Dec25 revised Using Quotient of Prime Numbers to Approximation Realsdeleted 59 characters in body; edited body Dec25 revised Using Quotient of Prime Numbers to Approximation Realsedited tags Dec25 revised Using Quotient of Prime Numbers to Approximation Realsadded 503 characters in body; added 78 characters in body; added 112 characters in body; added 90 characters in body Dec25 revised Using Quotient of Prime Numbers to Approximation Realsadded 82 characters in body; added 1 characters in body; added 17 characters in body Dec25 answered Using Quotient of Prime Numbers to Approximation Reals Dec18 comment maximum of the sum of polynomialsI am not sure I understand. On the interval $[0,1]$, take the polynomials $p_1(x)=x^2$ and $p_2(x)=(1-x)^2$. Each has maximum $1$, and exactly $1$ peak on this interval, but their sum has two peaks. For a more extreme example, take $p_1(x)=x$ and $p_2(x)=1-x$. Again, both have maximum $1$ and only $1$ peak on $[0,1]$, but their sum is then the constant function. Dec15 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$deleted 685 characters in body; added 144 characters in body Dec15 comment Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$Thanks for sharing this answer. It is much cleaner, and it made me realize I previously have an error in the calculation of the constant $C_0$. (Also, it certainly looks much nicer to write $S(n)=\frac{1}{\Gamma(-i)}n^{−i}\left(1+O\left(\frac{1}{n}\right)\right).$) Dec15 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 20 characters in body; deleted 6 characters in body; added 16 characters in body; edited body Dec15 comment Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$@S. Carnahan: Thank you for the response. However, I have noticed that I made a mistake in the calculation of the constant $C_0$. It should be around $0.3016$, not $0.33815$, and I can't find my error at the moment. If I don't find it soon, I will just delete my answer. Dec15 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 75 characters in body; added 50 characters in body Dec14 awarded ● Nice Answer Dec14 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 12 characters in body; deleted 18 characters in body; edited body Dec14 comment Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$@S. Carnahan: I don't believe so. Dec14 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 5 characters in body; added 57 characters in body; deleted 3 characters in body Dec14 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 22 characters in body Dec14 comment Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$@Noam D. Elkies: Thank you for pointing this out. I have updated my answer and added a proof. Dec14 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 511 characters in body; added 171 characters in body; added 37 characters in body; added 59 characters in body Dec14 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 244 characters in body; added 10 characters in body; deleted 2 characters in body; added 78 characters in body Dec14 revised Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$added 75 characters in body; added 14 characters in body; added 10 characters in body Dec14 answered Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$ Dec3 revised A curious limit involving prime numbers and composite numbersadded 46 characters in body Dec2 revised Integers represented by the polynomial $a^2+b^3+c^6$deleted 12 characters in body; edited title