Finding orientations of supersingular elliptic curves and quaternion orders

S Arpin, J Clements, P Dartois, JK Eriksen… - Designs, Codes and …, 2024‏ - Springer
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 …

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 …

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 …

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 …

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 …

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 …

Quartic polynomials in two variables do not represent all non-negative integers

SY **ao, S Yamagishi - arxiv preprint arxiv:2307.05712, 2023‏ - arxiv.org
arxiv:2307.05712v2 [math.NT] 13 Jul 2023 Page 1 arxiv:2307.05712v2 [math.NT] 13 Jul 2023
QUARTIC POLYNOMIALS IN TWO VARIABLES DO NOT REPRESENT ALL NON-NEGATIVE …

[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 …

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 …

Densities of integer sets represented by quadratic forms

PL Clark, P Pollack, J Rouse, K Thompson - Journal of Number Theory, 2024‏ - Elsevier
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 …