User davidlowryduda

36 votes

0 answers

865 views

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

asked Oct 2, 2013 at 3:48

17 votes

3 answers

3k views

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

sequences-and-series complex-analysis closed-form

asked Nov 3, 2011 at 19:50

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

asked Jan 31, 2012 at 6:03

15 votes

1 answer

782 views

Is there a 'far' irrational number?

number-theory analysis diophantine-approximation

asked Feb 14, 2012 at 18:02

14 votes

2 answers

3k views

Classifying Unital Commutative Rings of Order $p^2$

abstract-algebra ring-theory

asked Feb 15, 2012 at 3:40

11 votes

1 answer

7k views

Single Variable Calculus Reference Recommendations

calculus reference-request book-recommendation faq

asked Aug 18, 2014 at 4:27

8 votes

1 answer

279 views

Integrals 3.384 from Gradshteyn and Ryzhik

reference-request definite-integrals integration

asked Dec 10, 2013 at 1:19

8 votes

1 answer

295 views

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

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

asked Dec 13, 2012 at 8:37

7 votes

3 answers

317 views

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

number-theory quadratic-residues quadratic-reciprocity

asked Jul 7, 2014 at 22:24

6 votes

2 answers

785 views

Prime power Gauss sums are zero

number-theory analytic-number-theory gauss-sums

asked Apr 17, 2013 at 5:35

6 votes

1 answer

192 views

Dixon's Theorem to probabilistically bound largest factor of N

probability number-theory reference-request

asked Jul 25, 2011 at 8:06

6 votes

2 answers

797 views

Equivalent definitions of the trace of a Hilbert-Schmidt operator

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

asked Oct 21, 2014 at 20:25

6 votes

1 answer

225 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

asked Mar 27, 2015 at 21:28

6 votes

1 answer

3k views

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

real-analysis functional-analysis

asked May 2, 2016 at 19:51

5 votes

1 answer

1k views

Bounding error of Padé approximation

numerical-methods approximation-theory pade-approximation

asked Nov 17, 2014 at 5:33

5 votes

2 answers

164 views

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

number-theory elementary-number-theory prime-numbers

asked May 30, 2013 at 21:41

4 votes

2 answers

190 views

Looking for references on 'non-discrete lattices'

number-theory reference-request integer-lattices

asked Aug 13, 2013 at 10:51

4 votes

1 answer

107 views

A harder tournament to schedule

combinatorics elementary-number-theory

asked Sep 23, 2012 at 3:34

4 votes

1 answer

209 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

asked Nov 5, 2014 at 20:37

3 votes

4 answers

166 views

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

sequences-and-series summation asymptotics

asked Nov 15, 2015 at 2:30

3 votes

0 answers

82 views

Modular function for upper triangular matrices from Iwaniec

number-theory topological-groups haar-measure

asked Apr 20, 2021 at 16:37

3 votes

1 answer

144 views

Notation confusion in "On Some Results of Atkin and Lehner" article

notation automorphic-forms

asked May 1, 2012 at 21:48

3 votes

1 answer

406 views

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

measure-theory elementary-set-theory

asked May 30, 2012 at 0:47

3 votes

1 answer

232 views

A pair of integrals of rational powers of sines

calculus integration reference-request

asked Oct 8, 2014 at 23:30

2 votes

1 answer

495 views

Basic Monte Carlo simulation of indistinguishable balls and distinguishable bins

probability monte-carlo balls-in-bins

asked Sep 16, 2017 at 23:01

2 votes

2 answers

279 views

Estimating the sum of reciprocals of products of two primes

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

asked Jul 16, 2015 at 5:25

2 votes

1 answer

962 views

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

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

asked Sep 24, 2015 at 0:31

1 vote

1 answer

113 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

asked Sep 26, 2015 at 22:39

1 vote

0 answers

61 views

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

complex-analysis gamma-function

asked Dec 10, 2014 at 21:52

1 vote

2 answers

94 views

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

number-theory alternative-proof

asked Aug 29, 2012 at 6:08

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31 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

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

Prime power Gauss sums are zero

Dixon's Theorem to probabilistically bound largest factor of N

Equivalent definitions of the trace of a Hilbert-Schmidt operator

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]

Bounding error of Padé approximation

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

Looking for references on 'non-discrete lattices'

A harder tournament to schedule

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

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

Modular function for upper triangular matrices from Iwaniec

Notation confusion in "On Some Results of Atkin and Lehner" article

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

A pair of integrals of rational powers of sines

Basic Monte Carlo simulation of indistinguishable balls and distinguishable bins

Estimating the sum of reciprocals of products of two primes

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

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