User Chris

15 votes

1 answer

392 views

Closest cyclotomic integer to a cyclotomic number?

asked Jun 13, 2018 at 9:39

4 votes

3 answers

332 views

Finite sum $\sum_{k=1}^{p-1} \frac{1-\cos\left(\frac{2\pi k r}{p}\right)}{1-\cos\left(\frac{2\pi k s}{p}\right)}$ for $\gcd(p,rs)=1$.

asked Apr 18, 2018 at 16:46

4 votes

1 answer

58 views

Unit of the form $n\alpha + m \beta \sqrt{d}$ in real quadratic fields

asked Sep 25, 2018 at 12:11

4 votes

1 answer

133 views

Linear combination of two vectors in complex space

asked Jan 12, 2019 at 0:04

4 votes

3 answers

2k views

Expand $\cos^n (x)$ in terms of $\cos{kx}$, $k=1,\dots,n$.

asked Mar 30, 2017 at 15:30

4 votes

1 answer

397 views

Proof for known values of the Hermite constant

asked Mar 6, 2018 at 12:56

4 votes

1 answer

76 views

Which totally complex number field's embeddings correspond to geometric rotations/reflections in an argand diagram?

asked Apr 4, 2018 at 21:15

3 votes

1 answer

109 views

Determinant of a block matrix, blocks are transformations of the same matrix

asked Apr 12, 2018 at 13:36

2 votes

1 answer

95 views

Prove that $||u||\cdot ||v|| \geq |\langle u,v \rangle|$ for defined inner product

asked Mar 28, 2018 at 15:17

2 votes

1 answer

415 views

Norm-Euclidean Domains Division Algorithm

asked Oct 18, 2018 at 13:32

2 votes

1 answer

68 views

On the cardinality of rationals vs irrationals

asked Feb 7, 2019 at 22:35

2 votes

2 answers

194 views

The volume of an $n$-dimensional unit hypercube intersected with the plane $\sum_{i=1}^n x_i=0$.

asked Jan 4 at 18:32

2 votes

2 answers

507 views

Volume of an $n$-dimensional ellipsoid

asked Jul 17, 2018 at 21:09

1 vote

0 answers

34 views

A lower bound on the number of integer lattice points inside a 0-symmetric convex body

asked Jan 18 at 13:07

1 vote

0 answers

84 views

Determining Maximal Orders of a Quaternion Algebra

asked Nov 30, 2018 at 17:50

1 vote

1 answer

46 views

System of linear simultaneous equations

asked May 14, 2018 at 17:43

1 vote

1 answer

126 views

Multiplication over a cyclotomic field in terms of polynomials over the generators.

asked Jun 27, 2018 at 12:54

1 vote

1 answer

533 views

How does one define an inner product on the space $V=\mathbb{Q}_p^n$?

asked Jan 14, 2018 at 16:52

0 votes

1 answer

124 views

Calculate the integral $\int_{-1}^{1} \frac{(x-a)^2}{\sqrt{(1-x)}\ (1-ax)^4} dx$

asked Mar 30, 2017 at 12:46

0 votes

1 answer

81 views

Show that the set of elements of a field whose valuation is less than or equal to 1 is the ring of integers of that field.

asked Dec 21, 2017 at 15:43

0 votes

1 answer

173 views

Positive definite quadratic form over positive integer vectors

asked Jan 24, 2019 at 17:16

0 votes

1 answer

96 views

Maximising a multivariate linear function that includes the rounding in SAGE

asked Jul 26, 2021 at 17:20

0 votes

1 answer

38 views

Calculate the limit of a the following expression

asked Nov 8, 2022 at 13:44

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23 Questions

Closest cyclotomic integer to a cyclotomic number?

Finite sum $\sum_{k=1}^{p-1} \frac{1-\cos\left(\frac{2\pi k r}{p}\right)}{1-\cos\left(\frac{2\pi k s}{p}\right)}$ for $\gcd(p,rs)=1$.

Unit of the form $n\alpha + m \beta \sqrt{d}$ in real quadratic fields

Linear combination of two vectors in complex space

Expand $\cos^n (x)$ in terms of $\cos{kx}$, $k=1,\dots,n$.

Proof for known values of the Hermite constant

Which totally complex number field's embeddings correspond to geometric rotations/reflections in an argand diagram?

Determinant of a block matrix, blocks are transformations of the same matrix

Prove that $||u||\cdot ||v|| \geq |\langle u,v \rangle|$ for defined inner product

Norm-Euclidean Domains Division Algorithm

On the cardinality of rationals vs irrationals

The volume of an $n$-dimensional unit hypercube intersected with the plane $\sum_{i=1}^n x_i=0$.

Volume of an $n$-dimensional ellipsoid

A lower bound on the number of integer lattice points inside a 0-symmetric convex body

Determining Maximal Orders of a Quaternion Algebra

System of linear simultaneous equations

Multiplication over a cyclotomic field in terms of polynomials over the generators.

How does one define an inner product on the space $V=\mathbb{Q}_p^n$?

Calculate the integral $\int_{-1}^{1} \frac{(x-a)^2}{\sqrt{(1-x)}\ (1-ax)^4} dx$

Show that the set of elements of a field whose valuation is less than or equal to 1 is the ring of integers of that field.

Positive definite quadratic form over positive integer vectors

Maximising a multivariate linear function that includes the rounding in SAGE

Calculate the limit of a the following expression