Question

Hardy-Littlewood circle method applied to the binary problem

score 109 · Answer 1 · 2026-04-12 08:05:05

109

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Hardy-Littlewood circle method applied to the binary problem

Published on 12 Apr 2026 - 8:05

score 291 · Answer 2 · 2026-04-11 03:13:09

291

Views

Best known bounds on the error term for the average order of the sum-of-divisors function

Published on 11 Apr 2026 - 3:13

score 109 · Answer 3 · 2026-05-10 14:49:16

109

Views

Algebraic proof for $\sum_{r=1}^a\left\lfloor\frac{hr}k\right\rfloor+\sum_{r=1}^b\left\lfloor\frac{kr}h\right\rfloor=ab$

Published on 10 May 2026 - 14:49

score 181 · Answer 4 · 2026-05-10 11:02:19

181

Views

Theorem of Hardy & Ramanujan - second moment Method

Published on 10 May 2026 - 11:02

score 49 · Answer 5 · 2026-05-10 23:39:30

49

Views

Prove or refute that $\sum_{n=1}^\infty\frac{1}{n^2+A\varphi(n)+B}$ will be irrational for some choice of integers $A,B\geq 1$

Published on 10 May 2026 - 23:39

score 105 · Answer 6 · 2026-04-16 03:30:41

105

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If $m \ge 2n$, does $\binom{m}{n}$ always have prime factor greater than $n$?

Published on 16 Apr 2026 - 3:30

score 91 · Answer 7 · 2026-05-10 14:26:45

91

Views

Artin $L$-functions and abelianization

Published on 10 May 2026 - 14:26

score 103 · Answer 8 · 2026-05-10 20:57:48

103

Views

How to prove that $\sum_{k=1}^{am-1}\left\lfloor\frac ka\right\rfloor=a\sum_{k=1}^{m-1}k$?

Published on 10 May 2026 - 20:57

score 109 · Answer 9 · 2026-05-11 08:41:12

109

Views

What's $K$ (if it exists) in $\prod_{w \leq p < z} \left(1- \frac{1}{\phi(p)}\right)^{-1} \leq K \left(\frac{\log z}{\log w}\right)$?

Published on 11 May 2026 - 8:41

score 1.1k · Answer 10 · 2026-05-13 21:12:43

1.1k

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Convergence of Eisenstein series

Published on 13 May 2026 - 21:12

score 125 · Answer 11 · 2026-05-10 13:24:35

125

Views

Oscillations of a Mobius sum

Published on 10 May 2026 - 13:24

score 90 · Answer 12 · 2026-04-13 20:44:06

90

Views

Do you know a textbook that explains the series representations of the prime counting function?

Published on 13 Apr 2026 - 20:44

score 74 · Answer 13 · 2026-04-13 18:05:34

74

Views

Euler product on congruence classes

Published on 13 Apr 2026 - 18:05

score 200 · Answer 14 · 2026-04-14 20:57:09

200

Views

Show that $p_n^{1-\epsilon}\le n$ using PNT

Published on 14 Apr 2026 - 20:57

score 57 · Answer 15 · 2026-05-10 14:32:07

57

Views

Expressing an integer as the sum of three of more square free numbers.

Published on 10 May 2026 - 14:32

List Question

Hardy-Littlewood circle method applied to the binary problem

Best known bounds on the error term for the average order of the sum-of-divisors function

Algebraic proof for $\sum_{r=1}^a\left\lfloor\frac{hr}k\right\rfloor+\sum_{r=1}^b\left\lfloor\frac{kr}h\right\rfloor=ab$

Theorem of Hardy & Ramanujan - second moment Method

Prove or refute that $\sum_{n=1}^\infty\frac{1}{n^2+A\varphi(n)+B}$ will be irrational for some choice of integers $A,B\geq 1$

If $m \ge 2n$, does $\binom{m}{n}$ always have prime factor greater than $n$?

Artin $L$-functions and abelianization

How to prove that $\sum_{k=1}^{am-1}\left\lfloor\frac ka\right\rfloor=a\sum_{k=1}^{m-1}k$?

What's $K$ (if it exists) in $\prod_{w \leq p < z} \left(1- \frac{1}{\phi(p)}\right)^{-1} \leq K \left(\frac{\log z}{\log w}\right)$?

Convergence of Eisenstein series

Oscillations of a Mobius sum

Do you know a textbook that explains the series representations of the prime counting function?

Euler product on congruence classes

Show that $p_n^{1-\epsilon}\le n$ using PNT

Expressing an integer as the sum of three of more square free numbers.

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