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Results tagged with reference-request
Search options not deleted
user 48408
This tag is used if a reference is needed in a paper or textbook on a specific result.
6
votes
1
answer
672
views
Counting number of points in a lattice with bounded sup norm
Let $\Lambda$ be a lattice in $\mathbb{R}^n$. For $\bar{x} \in \mathbb{R}^n$, let
$\| \bar{x} \| = max_{1 \leq i \leq n} \{ |x_i| \}$, i.e. the sup norm. Let $\lambda_1, ..., \lambda_n$
be a successi …
- 579
3
votes
0
answers
195
views
Counting number of points in a lattice with bounded length
I am interested in counting number of lattices using the following theorem.
The following is Theorem IV (page 412) in Chapter VIII of "An introduction to the geometry of numbers (second printing, cor …
- 579
5
votes
2
answers
707
views
Sum of many squares modulo $n$
Let $n$ be a positive integer and $0 \leq i < n$. Define
$$
N(i) = \# \left\{ (x_1,\dots, x_s) \in [1, n]^s: x_1^2 +\dots + x_s^2 \equiv i \mod n \right\}.
$$
I am looking for a reference for the f …
- 579
1
vote
1
answer
246
views
Exponential sum estimates similar to the one for $\sum_p (\log p) e(p \alpha)$, but for diff...
Obtaining a non-trivial estimate for $\sum_p (\log p) e(p \alpha)$ over the minor arcs is one of the estimates required for obtaining the ternary Goldbach for $n$ sufficiently large via the circle met …
- 579