Nilotpal Sinha
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Registered User
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Fractal Analytics
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2d |
answered | Are sums of the inverses of prime siblings finite? |
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2d |
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Are sums of the inverses of prime siblings finite? If I understand your question correctly, you are asking the following. The sum of the reciprocal of primes is divergent but the sum of the reciprocal of twin primes is convergent (as shown by Brun). Your question is there any gap $d$ greater than 2 (2 is for twin primes) between primes for which the sum of the reciprocal primes differing by $d$ is convergent. Is this understanding correct? |
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May 20 |
comment |
Philosophy behind Yitang Zhang’s work on the Twin Primes Conjecture @Gerhard Paseman: I would rather NOT ask you about system design but I would definitely ask this question in this forum because if it is more than perfectly fitted here :) |
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May 18 |
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Sequences equidistributed modulo 1 But this is nothing but the extension of the Equidistributuion Theorem (first result) to polynomials, which was done my Weyl himself. So not just $n^2$, but any polynomial $s_n=f(n)$ is trivial. |
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May 18 |
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Sequences equidistributed modulo 1 added 408 characters in body |
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May 18 |
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Sequences equidistributed modulo 1 @Noam: While your example is correct, it is highly trivial because if we take $a$ to be normal in base $b$, then by the very definition of normality, we can construct similar example in that base $b$. Please note that in my examples of Weyl, Vonogradov had Hlawka, there is no such assumption on the normality constant which makes them non trivial. My question is can we have such a non trivial example such that $s_i/s_n$ does approach equidistribution modulo 1. |
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May 18 |
revised |
Sequences equidistributed modulo 1 deleted 2 characters in body; added 6 characters in body |
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May 18 |
asked | Sequences equidistributed modulo 1 |
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May 7 |
revised |
Square and reversed integer added 374 characters in body; added 89 characters in body |
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May 7 |
answered | Square and reversed integer |
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May 3 |
comment |
Why is it hard to prove that the Euler Mascheroni constant is irrational? "There are a lot more connections known between π and e and other numbers than between γ and other numbers." This may not entirely true. The numbers $e^{\gamma}$ pops up every now and then in the theory of primes. For example Merten's Theorems, Cramer-Granville's conjecture etc to name a few. But I do agree that the connection between $\gamma$ and other numbers that has nothing to do with primes directly or indirectly is far less common. |
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May 3 |
awarded | ● Yearling |
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Apr 28 |
revised |
A divergent series related to the number of divisors of of p-1 edited body |
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Apr 26 |
answered | Integer dynamics hitting infinitely many primes |
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Apr 25 |
answered | A divergent series related to the number of divisors of of p-1 |
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Mar 13 |
comment |
Multivariate functions whose value is independent of the order of the arguments @Survit: That practical application for which I need such a function has discrete arguments (positive integers) but we want to keep it flexible enough to accommodate all positive real values if required in future. |
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Mar 13 |
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Multivariate functions whose value is independent of the order of the arguments @Qiaochu: That is because the current application for which I need such a function has discrete arguments (positive integers) but we want to keep it flexible enough to accommodate all positive real values if required in future. |
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Mar 13 |
asked | Multivariate functions whose value is independent of the order of the arguments |
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Feb 28 |
awarded | ● Enthusiast |
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Feb 27 |
accepted | How can an integer be factorized as n*m so that n^m has the highest value. |
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Feb 27 |
answered | How can an integer be factorized as n*m so that n^m has the highest value. |
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Feb 21 |
awarded | ● Popular Question |
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Feb 20 |
revised |
Probability that randomly chosen integers from a restricted set of natural numbers are coprime edited tags |
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Feb 19 |
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Most inconsistent ranking @Kevin: Thanks for the insight and the lower bound. In my problem, I have a ranking system which gave me the rank matrix. In the best case when the ranking system is completely consistent, the variance of each row will be zero and hence the total sum will be zero. In my case I have a finite total sum of variance say $S$ and I want to compare it against the worst or the maximum possible total sum $S_{kn}$ in order to quantify how consistent the rank matrix is. I am updating this comment in the question. |
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Feb 19 |
revised |
Most inconsistent ranking added 521 characters in body; added 14 characters in body; deleted 3 characters in body |
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Feb 19 |
comment |
Most inconsistent ranking @Kevin: Yes this is the right understanding |
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Feb 19 |
revised |
Most inconsistent ranking added 92 characters in body; added 6 characters in body; edited tags |
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Feb 19 |
revised |
Most inconsistent ranking added 51 characters in body |
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Feb 19 |
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Most inconsistent ranking @ Gerry, I have now defined the sum of variance of the rows in condition number 2. |
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Feb 19 |
revised |
Most inconsistent ranking Define $S(k,n)$ after Gerry's comment; added 1 characters in body |
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Feb 19 |
asked | Most inconsistent ranking |
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Feb 17 |
awarded | ● Notable Question |
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Feb 14 |
awarded | ● Good Question |
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Feb 13 |
comment |
2^(p-1)-1 = 0 mod p^2 No conditions are known yet. |
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Feb 13 |
revised |
Mathematical techniques to reduce the amount of storage memory edited title |
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Feb 13 |
awarded | ● Mortarboard |
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Feb 12 |
awarded | ● Popular Question |
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Feb 12 |
awarded | ● Nice Answer |
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Feb 12 |
awarded | ● Nice Question |
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Feb 12 |
awarded | ● Self-Learner |
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Feb 12 |
answered | Mathematicians whose works were criticized by contemporaries but became widely accepted later |
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Feb 12 |
comment |
Mathematicians whose works were criticized by contemporaries but became widely accepted later @Yemon. No I had no such intention to distinguish between the two. All as wanted to know the lesser known mathematicians or stories that need to be heard. How do I make it community Wiki? |
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Feb 12 |
asked | Mathematicians whose works were criticized by contemporaries but became widely accepted later |
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Feb 11 |
awarded | ● Cleanup |
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Feb 11 |
revised |
On a sum involving prime numbers added 82 characters in body |
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Feb 11 |
awarded | ● Civic Duty |
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Feb 5 |
awarded | ● Disciplined |
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Feb 5 |
asked | Mathematical techniques to reduce the amount of storage memory |
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Feb 4 |
accepted | Sum involving binomial coefficients |
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Feb 4 |
comment |
Sum involving binomial coefficients @Pietro Yes there is such an integral which is in fact a contour integral. $$ s(n,r) = \frac{n!}{2\pi r!}\int_{|z|=1} z^{-n-1} \log^r (z+1)dz $$ @Danne, Yes I am sure. |
