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45 votes
7 answers
7k views

Swimming against the tide in the past century: remarkable achievements that arose in contrast to the general view of mathematicians

25 votes
3 answers
4k views

Evaluation of the quality of research articles submitted in mathematical journals: how do they do that?

14 votes
6 answers
5k views

The work of mathematicians outside their professional environment

13 votes
10 answers
1k views

References for literature from mathematicians who provided critiques and proposals concerning ethical aspects of mathematics research

12 votes
3 answers
725 views

Is $\sum_{n=1}^\infty\frac{S(n)}{n!}$ an irrational, where $S(n)$ denotes the sum of remainders function?

8 votes
0 answers
293 views

A generalization of Feit–Thompson conjecture, for square-free integers

7 votes
1 answer
198 views

The asymptotic of $|\{1\leq n\leq x|\gcd(n,S(n))=1\}|$, with $S(n)$ the sum of remainders, and get idea for other miscellany problem

7 votes
2 answers
404 views

Around the diophantine equation $\frac{a}{2b+3c}+\frac{b}{2c+3a}+\frac{c}{2a+3b}=\text{odd integer}$, over positive integers

7 votes
1 answer
805 views

On the closed-form of $\int_0^1\int_0^1\int_0^1\frac{dxdydz}{1-\frac{z}{3}(x+\sqrt{xy}+y)}$

7 votes
1 answer
642 views

Generalization of a problem, involving radicals and the floor function, proposed by Ramanujan to the Journal of the Indian Mathematical Society

6 votes
0 answers
251 views

Convergence with the recurrence $T_{n+1}=T_n^2-T_n+\frac{n}{p_n}$

6 votes
0 answers
88 views

Counterexamples or reasonings about the transcendence of series involving the Möbius function, and polynomials in the denominator

6 votes
2 answers
408 views

A generalization of strong primes

5 votes
0 answers
329 views

On a conjecture about the arithmetic function that counts the number of twin primes

5 votes
1 answer
332 views

Gadgets as primality tests

5 votes
1 answer
554 views

On the integral $\int_0^1\log(x!)dx$ revisited

5 votes
2 answers
461 views

What work can be done to study the solutions of $\varphi\left(x^{\sigma(x)}\sigma(x)^x\right)=2^{x-1} x^{3x-1}\varphi(x)$?

4 votes
1 answer
163 views

Products taken over semiprimes

4 votes
1 answer
215 views

The function $\sum_{n=0}^\infty\frac{(-1)^n\mu(2n+1)}{(2n+1)^s}$: reference request or particular values at integers and abscissa of convergence

4 votes
1 answer
299 views

What about $n^{\frac{1}{x}+\frac{1}{y}}+n^{\frac{1}{y}+\frac{1}{z}}=n^{\frac{1}{z}+\frac{1}{x}}$ over positive integers?

4 votes
2 answers
260 views

Express $\int_0^{\pi/2}\{ \operatorname{gd}^{-1}(x)\}dx$ as series of special functions, with $\operatorname{gd}^{-1}(z)$ the inverse Gudermannian

4 votes
0 answers
166 views

Near Pochhammer symbols: the equation $(n)_m-(k)_l=2$ for integers greater than or equal to two

4 votes
2 answers
351 views

Sharp estimates for Meissel-Mertens constant

4 votes
1 answer
278 views

A similar lemma to a lemma due to Lagarias, for the partial sums of reciprocal of primes

4 votes
1 answer
321 views

A principle around the Ramanujan's zeta function in short intervals

4 votes
2 answers
435 views

From Zurab's integral representation for the Apéry's constant to almost impossible integrals

3 votes
0 answers
137 views

Irrationality or transcendence of $i^{i\Omega}$ and $2^\Omega$, with $\Omega=W(1)$ and $W(x)$ being the main branch of Lambert $W$ function

3 votes
0 answers
137 views

On an inequality for the arithmetic function counting the number of primes $\lfloor n^c\rfloor$ in the spirit of Ramanujan's prime counting inequality

3 votes
1 answer
214 views

Around the equation $\sigma\left(\square\right)=\text{prime}$: counterexamples or a proof for some of these conjectures

3 votes
2 answers
413 views

Approximation of $\sum_{\rho}\frac{1}{|\rho|^2}$, over the non-trivial zeros of the Ramanujan's zeta function

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