User davidlowryduda

8

29

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757

views

Using the Brun Sieve to show very weak approximation to twin prime conjecture

Oct 4 '13 at 5:44 davidlowryduda♦ 78.6k

6

17

votes

3

answers

2k

views

closed form of $\sum \frac{1}{z^3 - n^3}$

sequences-and-series complex-analysis closed-form

Apr 14 at 5:44 William Ambrose 310

5

15

votes

1

answer

2k

views

$\frac{16}{27} \left( \frac a{b+c} + \frac b{a+c} +\frac c{a+b} \right) ^3 + \left( \frac{abc}{(a+b)(b+c)(a+c)}\right)^{\frac{1}{3}} \geq \frac52$

inequality contest-math

Nov 2 '16 at 6:45 Michael Rozenberg 143k

2

15

votes

1

answer

755

views

Is there a 'far' irrational number?

number-theory analysis diophantine-approximation

Feb 14 '12 at 20:09 Aryabhata 73.9k

3

14

votes

2

answers

2k

views

Classifying Unital Commutative Rings of Order $p^2$

abstract-algebra ring-theory

Feb 15 '12 at 8:45 Pete L. Clark 85.4k

17

9

votes

1

answer

5k

views

Single Variable Calculus Reference Recommendations

calculus reference-request book-recommendation faq

Aug 18 '14 at 5:11 Community♦ 1

4

8

votes

1

answer

226

views

Integrals 3.384 from Gradshteyn and Ryzhik

reference-request definite-integrals integration

Sep 6 at 14:25 Maximilian Janisch 7,586

2

7

votes

1

answer

225

views

Invariants of binary forms under a $\begin{pmatrix} 1& 1 \\ 0& 1 \end{pmatrix}$ action

group-theory reference-request group-actions invariant-theory

Dec 14 '12 at 7:06 davidlowryduda♦ 78.6k

2

6

votes

1

answer

181

views

In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

calculus terminology math-history

Jan 9 '17 at 17:23 Will M. 3,487

2

6

votes

1

answer

1k

views

Do there exist bump functions with uniformly bounded derivatives? [duplicate]

real-analysis functional-analysis

May 2 '16 at 20:05 zhw. 83.3k

6

votes

2

answers

588

views

Prime power Gauss sums are zero

number-theory analytic-number-theory gauss-sums

Aug 13 '15 at 17:26 Greg Doyle 173

2

6

votes

3

answers

244

views

Elementary, direct proof of when $5$ is a quadratic residue mod $p$

number-theory quadratic-residues quadratic-reciprocity

Jan 17 '15 at 4:04 Community♦ 1

6

votes

1

answer

167

views

Dixon's Theorem to probabilistically bound largest factor of N

probability number-theory reference-request

Jul 25 '11 at 15:32 davidlowryduda♦ 78.6k

5

votes

1

answer

785

views

Bounding error of Padé approximation

numerical-methods approximation-theory pade-approximation

Oct 6 '17 at 18:35 Tobias Kienzler 5,565

2

5

votes

2

answers

154

views

Choosing $a$ s.t. $\frac{a^k - 1}{a-1}$ is not a prime power

number-theory elementary-number-theory prime-numbers

May 31 '13 at 2:18 Zander 10.4k

3

4

votes

2

answers

534

views

Equivalent definitions of the trace of a Hilbert-Schmidt operator

functional-analysis operator-theory hilbert-spaces compact-operators trace

Oct 29 '18 at 17:59 punctured dusk 20.1k

4

votes

1

answer

81

views

Proving that $(2 \pi i)^{-1} \int e(\pi v^2/y^2) x^v y^{-1} dv = e(-\pi (\log x)^2 y^2 /4)$

integration analytic-number-theory integral-transforms

Nov 4 '15 at 4:05 davidlowryduda♦ 78.6k

4

votes

2

answers

129

views

Looking for references on 'non-discrete lattices'

number-theory reference-request integer-lattices

Aug 13 '13 at 14:14 paul garrett 33.9k

4

votes

1

answer

93

views

A harder tournament to schedule

combinatorics elementary-number-theory

Sep 23 '12 at 4:39 davidlowryduda♦ 78.6k

1

3

votes

4

answers

133

views

Estimating an exponential sum $\sum_{n = 1}^x e^n/n$

sequences-and-series summation asymptotics

Jun 5 '17 at 23:19 Simply Beautiful Art 62.8k

3

votes

1

answer

149

views

A pair of integrals of rational powers of sines

calculus integration reference-request

Oct 9 '14 at 2:02 Lucian 44.4k

3

votes

1

answer

331

views

Finding an irrational not covered in standard proof that $\mu(\mathbb{Q} \cap [0,1]) = 0$ [duplicate]

measure-theory elementary-set-theory

May 30 '12 at 6:54 Community♦ 1

1

2

votes

1

answer

659

views

Expected distance of a random walk of distance $k$ on the $k$th step

probability random-variables random-walk central-limit-theorem

Dec 10 at 14:56 Filip 111

1

2

votes

1

answer

306

views

Basic Monte Carlo simulation of indistinguishable balls and distinguishable bins

probability monte-carlo balls-in-bins

Sep 16 '17 at 23:26 Steve Kass 12.6k

2

votes

3

answers

185

views

Estimating the sum of reciprocals of products of two primes

sequences-and-series number-theory convergence-divergence analytic-number-theory

Jul 16 '15 at 9:58 Marco Cantarini 30.2k

1

2

votes

1

answer

111

views

Notation confusion in “On Some Results of Atkin and Lehner” article

notation automorphic-forms

May 1 '12 at 22:10 anon 75.9k

1

vote

1

answer

101

views

Showing that $\int_0^1 \vert 1 - e^{2\pi i z} \vert^{-1} dx \ll \log(2 + y^{-1})$

calculus integration definite-integrals analytic-number-theory

Sep 26 '15 at 23:13 Jack D'Aurizio 312k

1

vote

0

answers

57

views

Proving a bound for $\Gamma(s+u)/\Gamma(s)$

complex-analysis gamma-function

Dec 10 '14 at 21:52 davidlowryduda♦ 78.6k

1

vote

2

answers

80

views

Showing that $\{ n\mid \nu(n) \equiv 0 \pmod e\}$ is independent of primitive root

number-theory alternative-proof

Aug 29 '12 at 7:09 Marc van Leeuwen 94.7k

1

vote

1

answer

141

views

Trying to construct a function to 'Distribute the Integral'

calculus

Feb 23 '12 at 22:03 Arturo Magidin 291k

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30 Questions

Using the Brun Sieve to show very weak approximation to twin prime conjecture

closed form of $\sum \frac{1}{z^3 - n^3}$

$\frac{16}{27} \left( \frac a{b+c} + \frac b{a+c} +\frac c{a+b} \right) ^3 + \left( \frac{abc}{(a+b)(b+c)(a+c)}\right)^{\frac{1}{3}} \geq \frac52$

Is there a 'far' irrational number?

Classifying Unital Commutative Rings of Order $p^2$

Single Variable Calculus Reference Recommendations

Integrals 3.384 from Gradshteyn and Ryzhik

Invariants of binary forms under a $\begin{pmatrix} 1& 1 \\ 0& 1 \end{pmatrix}$ action

In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

Do there exist bump functions with uniformly bounded derivatives? [duplicate]

Prime power Gauss sums are zero

Elementary, direct proof of when $5$ is a quadratic residue mod $p$

Dixon's Theorem to probabilistically bound largest factor of N

Bounding error of Padé approximation

Choosing $a$ s.t. $\frac{a^k - 1}{a-1}$ is not a prime power

Equivalent definitions of the trace of a Hilbert-Schmidt operator

Proving that $(2 \pi i)^{-1} \int e(\pi v^2/y^2) x^v y^{-1} dv = e(-\pi (\log x)^2 y^2 /4)$

Looking for references on 'non-discrete lattices'

A harder tournament to schedule

Estimating an exponential sum $\sum_{n = 1}^x e^n/n$

A pair of integrals of rational powers of sines

Finding an irrational not covered in standard proof that $\mu(\mathbb{Q} \cap [0,1]) = 0$ [duplicate]

Expected distance of a random walk of distance $k$ on the $k$th step

Basic Monte Carlo simulation of indistinguishable balls and distinguishable bins

Estimating the sum of reciprocals of products of two primes

Notation confusion in “On Some Results of Atkin and Lehner” article

Showing that $\int_0^1 \vert 1 - e^{2\pi i z} \vert^{-1} dx \ll \log(2 + y^{-1})$

Proving a bound for $\Gamma(s+u)/\Gamma(s)$

Showing that $\{ n\mid \nu(n) \equiv 0 \pmod e\}$ is independent of primitive root

Trying to construct a function to 'Distribute the Integral'