Finding orientations of supersingular elliptic curves and quaternion orders
An oriented supersingular elliptic curve is a curve which is enhanced with the information of
an endomorphism. Computing the full endomorphism ring of a supersingular elliptic curve is …
an endomorphism. Computing the full endomorphism ring of a supersingular elliptic curve is …
Sums of two squares and the tau-function: Ramanujan's trail
BC Berndt, P Moree - arXiv preprint arXiv:2409.03428, 2024 - arxiv.org
Ramanujan, in his famous first letter to Hardy, claimed a very precise estimate for the
number of integers that can be written as a sum of two squares. Far less well-known is that …
number of integers that can be written as a sum of two squares. Far less well-known is that …
Quartic polynomials in two variables do not represent all non-negative integers
SY Xiao, S Yamagishi - arXiv preprint arXiv:2307.05712, 2023 - arxiv.org
arXiv:2307.05712v1 [math.NT] 11 Jul 2023 Page 1 arXiv:2307.05712v1 [math.NT] 11 Jul 2023
QUARTIC POLYNOMIALS IN TWO VARIABLES DO NOT REPRESENT ALL NON-NEGATIVE …
QUARTIC POLYNOMIALS IN TWO VARIABLES DO NOT REPRESENT ALL NON-NEGATIVE …
Counting numbers in multiplicative sets: Landau versus Ramanujan
P Moree - arXiv preprint arXiv:1110.0708, 2011 - arxiv.org
A set S of integers is said to be multiplicative if for every pair m and n of coprime integers we
have that mn is in S iff both m and n are in S. Both Landau and Ramanujan gave …
have that mn is in S iff both m and n are in S. Both Landau and Ramanujan gave …
[HTML][HTML] The lengths of Hermitian self-dual extended duadic codes
L Dicuangco, P Moree, P Solé - Journal of Pure and Applied Algebra, 2007 - Elsevier
Duadic codes are a class of cyclic codes that generalize quadratic residue codes from prime
to composite lengths. For every prime power q, we characterize integers n such that there is …
to composite lengths. For every prime power q, we characterize integers n such that there is …
On the finiteness of the classifying space for virtually cyclic subgroups
TW von Puttkamer - 2018 - bonndoc.ulb.uni-bonn.de
This thesis mainly deals with finiteness properties of the classifying space for the family of
virtually cyclic subgroups. We establish a link between the finiteness of the classifying space …
virtually cyclic subgroups. We establish a link between the finiteness of the classifying space …
Biases Towards the Zero Residue Class for Quadratic Forms in Arithmetic Progressions
J Schlitt - arXiv preprint arXiv:2308.13959, 2023 - arxiv.org
We examine a bias towards the zero residue class for the integers represented by binary
quadratic forms. In many cases, we are able to prove that the bias comes from a secondary …
quadratic forms. In many cases, we are able to prove that the bias comes from a secondary …
Principal forms X 2+nY 2 representing many integers
D Brink, P Moree, R Osburn - Abhandlungen aus dem Mathematischen …, 2011 - Springer
Abstract In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of
positive integers less than or equal to x which are represented by the quadratic form X 2+ nY …
positive integers less than or equal to x which are represented by the quadratic form X 2+ nY …
Fast multi-precision computation of some Euler products
S Ettahri, O Ramaré, L Surel - Mathematics of Computation, 2021 - ams.org
For every modulus $ q\ge 3$, we define a family of subsets $\mathcal {A} $ of the
multiplicative group $(\mathbb {Z}/q\mathbb {Z})^\times $ for which the Euler product $\prod …
multiplicative group $(\mathbb {Z}/q\mathbb {Z})^\times $ for which the Euler product $\prod …
Densities of integer sets represented by quadratic forms
Abstract Let f (t 1,…, tn) be a nondegenerate integral quadratic form. We analyze the
asymptotic behavior of the function D f (X), the number of integers of absolute value up to X …
asymptotic behavior of the function D f (X), the number of integers of absolute value up to X …