Eric Naslund
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Registered User
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My interests lean towards Analytic Number Theory and Additive Combinatorics.
You can contact me at: naslund (at) princeton.edu |
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Apr 18 |
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Estimates for the size of the product set [n].[n] This is an exact duplicate of: mathoverflow.net/questions/108912/… |
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Mar 25 |
answered | Recovering $\sum_{n \leq x} a(n)$ from $\sum_{n \leq x} a(n)e^{-n/x}$ |
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Mar 19 |
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Probability that two random integers are coprime See the last part of this Math Stack Exchange answer: math.stackexchange.com/a/38142/6075 |
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Mar 18 |
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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?" |
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Mar 12 |
awarded | ● Popular Question |
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Mar 12 |
revised |
Integer Points on the Elliptic Curve $y^2=x^3+17$. deleted 243 characters in body; edited title |
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Mar 12 |
revised |
Mathematical Advice for Interested Highschool Students deleted 61 characters in body |
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Mar 1 |
awarded | ● Popular Question |
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Mar 1 |
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Euler constant transcendality. The question of irrationality is still open. See: en.wikipedia.org/wiki/… |
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Mar 1 |
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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. |
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Mar 1 |
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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. |
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Mar 1 |
accepted | How to rewrite this totient summation in terms of Mertens? |
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Mar 1 |
answered | How to rewrite this totient summation in terms of Mertens? |
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Feb 19 |
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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 $$\sqrt{3.206*10^{11}}/\log(3.206*10^{11})\approx 21371.$$ |
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Feb 3 |
accepted | A curious limit involving prime numbers and composite numbers |
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Feb 1 |
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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 $10^9$. |
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Feb 1 |
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Should I tell my coauthor? This may be more appropriate on academia.stackexchange.com |
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Jan 20 |
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Probability of all combinations of k numbers among n being coprime How are the $x_1,\dots,x_n$ chosen? If they are all multiples of two, then the gcd condition never happens. |
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Jan 12 |
awarded | ● Yearling |
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Jan 3 |
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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. |
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Dec 31 |
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3-7 primes in base 10 Can we even prove that there are infinitely many primes which in their decimal expansion do not contain the digit $9$? |
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Dec 25 |
revised |
Using Quotient of Prime Numbers to Approximation Reals added 166 characters in body; added 57 characters in body; deleted 6 characters in body |
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Dec 25 |
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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. |
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Dec 25 |
revised |
Using Quotient of Prime Numbers to Approximation Reals added 1 characters in body |
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Dec 25 |
awarded | ● Enlightened |
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Dec 25 |
awarded | ● Nice Answer |
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Dec 25 |
accepted | Using Quotient of Prime Numbers to Approximation Reals |
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Dec 25 |
revised |
Using Quotient of Prime Numbers to Approximation Reals deleted 59 characters in body; edited body |
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Dec 25 |
revised |
Using Quotient of Prime Numbers to Approximation Reals edited tags |
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Dec 25 |
revised |
Using Quotient of Prime Numbers to Approximation Reals added 503 characters in body; added 78 characters in body; added 112 characters in body; added 90 characters in body |
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Dec 25 |
revised |
Using Quotient of Prime Numbers to Approximation Reals added 82 characters in body; added 1 characters in body; added 17 characters in body |
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Dec 25 |
answered | Using Quotient of Prime Numbers to Approximation Reals |
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Dec 18 |
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maximum of the sum of polynomials I 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. |
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Dec 15 |
revised |
Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$ deleted 685 characters in body; added 144 characters in body |
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Dec 15 |
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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 $S(n)=\frac{1}{\Gamma(-i)}n^{−i}\left(1+O\left(\frac{1}{n}\right)\right).$) |
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Dec 15 |
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 |
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Dec 15 |
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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. |
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Dec 15 |
revised |
Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$ added 75 characters in body; added 50 characters in body |
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Dec 14 |
awarded | ● Nice Answer |
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Dec 14 |
revised |
Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$ added 12 characters in body; deleted 18 characters in body; edited body |
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Dec 14 |
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Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$ @S. Carnahan: I don't believe so. |
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Dec 14 |
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 |
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Dec 14 |
revised |
Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$ added 22 characters in body |
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Dec 14 |
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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. |
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Dec 14 |
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 |
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Dec 14 |
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 |
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Dec 14 |
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 |
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Dec 14 |
answered | Combinatorial interpretation of ${i\choose n}$, where $i^2=-1$ |
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Dec 3 |
revised |
A curious limit involving prime numbers and composite numbers added 46 characters in body |
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Dec 2 |
revised |
Integers represented by the polynomial $a^2+b^3+c^6$ deleted 12 characters in body; edited title |
