User Vik78

1 vote

1 answer

83 views

What’s the best bound on the Dirichlet coefficients of $\zeta(s-1)^2/\zeta(s)$

asked Mar 3, 2023 at 15:53

1 vote

1 answer

83 views

Even functions absorb composition?

asked May 24, 2016 at 3:56

1 vote

0 answers

80 views

Question from Herstein's Topics in Algebra on Sylow subgroups [duplicate]

asked Aug 29, 2016 at 23:19

1 vote

1 answer

79 views

Suppose $f^{(k)}(0) = 0$ for all $k \ge 0$, where $f$ is $C^\infty$. Is 0 then an accumulation point of a set where $f$ vanishes?

asked Jan 13, 2017 at 14:37

3 votes

1 answer

76 views

Is there an interesting example of a chaotic dynamical system on $\widehat{\mathbb{C}}^n$, where $\widehat{\mathbb{C}}$ is the Riemann sphere?

asked Jan 12, 2022 at 22:10

1 vote

0 answers

76 views

Jacobian criterion for Zariski cotangent space over arbitrary field

asked Jun 23, 2023 at 17:00

4 votes

0 answers

65 views

Is there a name for this graph-theoretic concept?

asked Feb 21, 2016 at 16:09

2 votes

1 answer

60 views

Let $p, q \in k[x_1,...,x_n]$ with no common divisor. Must there exist $a, b \in k$ so $ap + bq$ is irreducible?

asked Apr 25, 2022 at 12:13

1 vote

1 answer

55 views

Find antiderivative of $ln(x)^y$ for any real y

asked May 25, 2016 at 17:23

0 votes

0 answers

53 views

How does the cardinality of the set of all functions from $A$ to itself relate to that of $A$?

asked May 13, 2016 at 18:41

2 votes

1 answer

51 views

Discrete sums are to integrals as discrete products are to ___. [duplicate]

asked Feb 29, 2016 at 5:11

2 votes

0 answers

51 views

We know the asymptotic density of primes. What about the asymptotic density of numbers with n prime factors? [duplicate]

asked Mar 13, 2016 at 15:14

0 votes

1 answer

50 views

Probability that polynomial $f(m)$ is prime for $m < n$, as $n$ goes to infinity?

asked Mar 6, 2016 at 2:22

2 votes

0 answers

48 views

Can one show that in a certain sense, "most" polynomials have Galois group $S_n$? [duplicate]

asked May 18, 2022 at 23:30

2 votes

0 answers

44 views

van der Waerden's proof that a monic $p(x) \in \mathbb{Z}[x]$ has Galois group $S_n$ with probability 1

asked May 19, 2022 at 1:35

1 vote

1 answer

43 views

Example of set with irrational upper arithmetic density?

asked Jan 31, 2016 at 17:05

2 votes

0 answers

41 views

Can anyone give an example of a set of numbers with arithmetic density that doesn't converge to a limit?

asked May 23, 2016 at 2:12

0 votes

0 answers

40 views

When can a function be represented by an infinite nested radical, a la a Taylor series?

asked Feb 29, 2016 at 5:22

0 votes

1 answer

37 views

If $\alpha \in BV[a, b]$, $\int_a^b fd\alpha$ exists and $\alpha$ is continuous at $x \in [a, b]$, $F(y) = \int_a^y f d\alpha$ is continuous at $x$

asked Mar 10, 2017 at 17:37

0 votes

0 answers

36 views

Find sequences $(a_n)$, $(b_n)$ such that $(b_n)$ is positive and decreasing, the sum over $(a_n)$ converges, and the sum over $(a_nb_n)$ diverges

asked Oct 23, 2016 at 0:07

1 vote

0 answers

33 views

Let $p, q \in k[x_1,...,x_n]$ with no common divisor, $n\ge3$ (and a nontriviality condition). Must $\exists a, b \in k$ so $ap + bq$ is irreducible?

asked Apr 25, 2022 at 15:44

0 votes

0 answers

31 views

If $f$ is analytic on an open connected set, is it equal everywhere to the power series around any point?

asked Oct 1, 2016 at 19:12

1 vote

0 answers

28 views

Making polynomial irreducible by adding term of given arithmetic progression

asked Mar 6, 2016 at 3:37

0 votes

1 answer

28 views

Is a convergent power series on an open set continuous on that set?

asked Apr 16, 2016 at 22:30

0 votes

0 answers

25 views

Are there any integral domains in which irreducible elements are easily identified?

asked May 6, 2016 at 5:05

0 votes

1 answer

24 views

Let $(a_n)$ be a sequence such that for any $(b_n) \in l^1$, $(a_nb_n) \in l^1$. Show $(a_n)$ is bounded.

asked Nov 14, 2016 at 5:18

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86 Questions

What’s the best bound on the Dirichlet coefficients of $\zeta(s-1)^2/\zeta(s)$

Even functions absorb composition?

Question from Herstein's Topics in Algebra on Sylow subgroups [duplicate]

Suppose $f^{(k)}(0) = 0$ for all $k \ge 0$, where $f$ is $C^\infty$. Is 0 then an accumulation point of a set where $f$ vanishes?

Is there an interesting example of a chaotic dynamical system on $\widehat{\mathbb{C}}^n$, where $\widehat{\mathbb{C}}$ is the Riemann sphere?

Jacobian criterion for Zariski cotangent space over arbitrary field

Is there a name for this graph-theoretic concept?

Let $p, q \in k[x_1,...,x_n]$ with no common divisor. Must there exist $a, b \in k$ so $ap + bq$ is irreducible?

Find antiderivative of $ln(x)^y$ for any real y

How does the cardinality of the set of all functions from $A$ to itself relate to that of $A$?

Discrete sums are to integrals as discrete products are to ___. [duplicate]

We know the asymptotic density of primes. What about the asymptotic density of numbers with n prime factors? [duplicate]

Probability that polynomial $f(m)$ is prime for $m < n$, as $n$ goes to infinity?

Can one show that in a certain sense, "most" polynomials have Galois group $S_n$? [duplicate]

van der Waerden's proof that a monic $p(x) \in \mathbb{Z}[x]$ has Galois group $S_n$ with probability 1

Example of set with irrational upper arithmetic density?

Can anyone give an example of a set of numbers with arithmetic density that doesn't converge to a limit?

When can a function be represented by an infinite nested radical, a la a Taylor series?

If $\alpha \in BV[a, b]$, $\int_a^b fd\alpha$ exists and $\alpha$ is continuous at $x \in [a, b]$, $F(y) = \int_a^y f d\alpha$ is continuous at $x$

Find sequences $(a_n)$, $(b_n)$ such that $(b_n)$ is positive and decreasing, the sum over $(a_n)$ converges, and the sum over $(a_nb_n)$ diverges

Let $p, q \in k[x_1,...,x_n]$ with no common divisor, $n\ge3$ (and a nontriviality condition). Must $\exists a, b \in k$ so $ap + bq$ is irreducible?

If $f$ is analytic on an open connected set, is it equal everywhere to the power series around any point?

Making polynomial irreducible by adding term of given arithmetic progression

Is a convergent power series on an open set continuous on that set?

Are there any integral domains in which irreducible elements are easily identified?

Let $(a_n)$ be a sequence such that for any $(b_n) \in l^1$, $(a_nb_n) \in l^1$. Show $(a_n)$ is bounded.