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If you are asking a question about the mean value of a multiplicative function, I encourage you to read these two answers:

  • http://math.stackexchange.com/questions/90120/mean-value-of-a-multiplicative-function-close-to-n-in-terms-of-the-zeta-functi/90125#90125
  • http://math.stackexchange.com/questions/84708/prove-sum-limits-n-leq-x-fracn-phin-ox/84721#84721
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Top Questions
272 votes

The Mathematics of Tetris

recreational-mathematics problem-solving packing-problem parity invariance asked Nov 8 '11 at 16:51
math.stackexchange.com

158 votes

What are examples of very aggressive openings?

opening aggressive-play asked May 2 '12 at 10:24
chess.stackexchange.com

65 votes

Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$

calculus limits radicals faq indeterminate-forms asked Mar 31 '11 at 1:34
math.stackexchange.com

52 votes

When has the Borel-Cantelli heuristic been wrong?

nt.number-theory pr.probability real-analysis analytic-number-theory big-list asked Apr 15 '15 at 20:31
mathoverflow.net

46 votes

Getting the expectation symbol to behave like $\sum$ instead of $\Sigma$

math-mode math-operators asked May 21 '12 at 12:34
tex.stackexchange.com

37 votes

Fermat's Last Theorem and Kummer's Objection

number-theory ring-theory algebraic-number-theory field-theory factoring asked Nov 25 '11 at 13:47
math.stackexchange.com

35 votes

A series problem by Knuth

sequences-and-series approximation gamma-function factorial asked Aug 29 '11 at 15:24
math.stackexchange.com

33 votes

An Entropy Inequality

pr.probability real-analysis inequalities it.information-theory entropy asked Jul 31 '13 at 21:03
mathoverflow.net

32 votes

Explicitly reconstructing a function from its moments

complex-analysis fourier-analysis asked Apr 13 '11 at 3:59
math.stackexchange.com

30 votes

The Erdős-Turán conjecture or the Erdős' conjecture?

additive-combinatorics nt.number-theory reference-request ho.history-overview erdos asked Jun 3 '13 at 15:03
mathoverflow.net

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Top Answers
366
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
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154
$\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
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128
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
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104
100 Soldiers riddle
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90
What is special about the numbers 9801, 998001, 99980001 ..?
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87
Prove $2^{1/3}$ is irrational.
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79
What is so interesting about the zeroes of the Riemann $\zeta$ function?
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74
A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$
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72
When log is written without a base, is the equation normally referring to log base 10 or natural log?
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Number of elements in the set $\{1,\cdots,n\}\cdot\{1,\cdots,n\}$
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61
How to effectively and efficiently learn mathematics
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The staircase paradox, or why $\pi\ne4$
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52
How to sum this series for $\pi/2$ directly?
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52
Prove every odd integer is the difference of two squares
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49
Proof of 1 = 0 by Mathematical Induction on Limits?
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48
Examples of seemingly elementary problems that are hard to solve?
mathoverflow.net

42
How do I get the square root of a complex number?
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42
Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded?
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42
Does Zhang's theorem generalize to $3$ or more primes in an interval of fixed length?
mathoverflow.net

41
How to prove that eigenvectors from different eigenvalues are linearly independent
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41
What is the smallest unknown natural number?
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38
What is the difference between max and sup?
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37
What is the crucial difference the Maynard/Tao approach and Goldston-Pintz-Yildirim that extends to prime k-tuples with $k>2$
mathoverflow.net

36
Probability that two random numbers are coprime is $\frac{6}{\pi^2}$
math.stackexchange.com

35
A pencil approach to find $\sum \limits_{i=1}^{69} \sqrt{\left( 1+\frac{1}{i^2}+\frac{1}{(i+1)^2}\right)}$
math.stackexchange.com

32
Primes of the form $n^2+1$ - hard?
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31
How does $ \sum_{p<x} p^{-s} $ grow asymptotically for $ \text{Re}(s) < 1 $?
math.stackexchange.com

30
How to show $\lim_{n \to \infty} a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} = x/2$?
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Importance of rigor
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Real life examples for eigenvalues / eigenvectors
math.stackexchange.com

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