List questions from analytic-number-theory

Published on 30 Mar 2026 - 4:25

394

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Prove that von Mangoldt function satisfies $\sum_{n \le x} \Lambda(n) \lfloor{\frac{x}{n}}\rfloor= x \ln(x)-x+O(\ln x)$

Published on 22 Jul 2019 - 5:21

71

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Prove that the asymptotic density of $w(n)|n$ is 0

Published on 23 Jul 2019 - 5:13

45

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Why is the following equality involving big $O$-notation true?

Published on 27 Jul 2019 - 14:06

92

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Generalization on a feature of 21

Published on 27 Mar 2026 - 2:59

139

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Why does this interval contain at least $x/(5\log(x))$ primes?

Published on 02 Aug 2019 - 19:58

159

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For the divisor function is $d(n^2)$ related to $d(n)$ knowing also n?

Published on 25 Mar 2026 - 17:26

62

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Polya-Vinogradov inequality over non-consecutive integers

Published on 04 Aug 2019 - 6:01

38

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Non-vanishing Taylor coefficients and Poincaré series

Published on 28 Mar 2026 - 12:49

59

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Bounding coefficients of Dirichlet Series

Published on 25 Mar 2026 - 9:38

221

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Curious closed forms of the $q$-Gamma function.

Published on 25 Mar 2026 - 9:47

106

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Heuristics on the Circle Method

Published on 10 Aug 2019 - 17:05

66

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Simplifying an alternating sum of a product of factorials

Published on 27 Mar 2026 - 5:39

138

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How was this formula made by Srinavasa Ramanujan derived?

Published on 27 Mar 2026 - 20:20

49

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A curious identity summing over primes in an interval.

Published on 15 Aug 2019 - 14:16

List Question

Regarding definitions of modular functions and modular forms

Prove that von Mangoldt function satisfies $\sum_{n \le x} \Lambda(n) \lfloor{\frac{x}{n}}\rfloor= x \ln(x)-x+O(\ln x)$

Prove that the asymptotic density of $w(n)|n$ is 0

Why is the following equality involving big $O$-notation true?

Generalization on a feature of 21

Why does this interval contain at least $x/(5\log(x))$ primes?

For the divisor function is $d(n^2)$ related to $d(n)$ knowing also n?

Polya-Vinogradov inequality over non-consecutive integers

Non-vanishing Taylor coefficients and Poincaré series

Bounding coefficients of Dirichlet Series

Curious closed forms of the $q$-Gamma function.

Heuristics on the Circle Method

Simplifying an alternating sum of a product of factorials

How was this formula made by Srinavasa Ramanujan derived?

A curious identity summing over primes in an interval.

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