Results 281 to 290 of about 190,388 (322)
Some of the next articles are maybe not open access.
Indecomposable binary quadratic forms
Archiv der Mathematik, 1991The paper contains the following proposition: Let \(d>4\) and \(d\equiv 2 \bmod 4\) then there does not exist an indecomposable definite binary quadratic form with discriminant \(d\) iff the number of classes in each genus of binary quadratic forms with discriminant \(d\) is 1.
openaire +2 more sources
GONI: PRIMES REPRESENTED BY BINARY QUADRATIC FORMS
2014We list 2779 regular primitive positive definite integral binary quadratic forms, and show that, conditional on the Generalized Riemann Hypothesis, this is the complete list of regular, positive definite binary integral quadratic forms (up to SL2(Z)-equivalence).
Clark, Pete L. +3 more
openaire +2 more sources
Exceptional Integers for Binary Quadratic Forms
Journal of Mathematical Sciences, 2001Let \(C\) be a class of primitive binary quadratic forms, and let \(R\) be the genus containing \(C\). A number is said to be exceptional for \(C\) if it is representable by a form in \(R\) but not by a form in \(C\). The author establishes an asymptotic distribution law for exceptional numbers which extends an earlier result of \textit{O. M. Fomenko} [
openaire +2 more sources
1986
An integral function is a sum of the form $$ F = \Sigma {c_{{\alpha _1} \cdots {\alpha _n}}}x_1^{{\alpha _1}} \ldots x_n^{{\alpha _n}} $$ where $$ {c_{{\alpha _1}}}{ \ldots _{{\alpha _1}}} $$ is an integer constant and \({\alpha _1}, \ldots ,{\alpha _n}\) are non negative integers.
openaire +1 more source
An integral function is a sum of the form $$ F = \Sigma {c_{{\alpha _1} \cdots {\alpha _n}}}x_1^{{\alpha _1}} \ldots x_n^{{\alpha _n}} $$ where $$ {c_{{\alpha _1}}}{ \ldots _{{\alpha _1}}} $$ is an integer constant and \({\alpha _1}, \ldots ,{\alpha _n}\) are non negative integers.
openaire +1 more source
Composition of Binary Quadratic Forms
Resonance, 2019In 2004, Bhargava introduced a new way to understand the composition law of integral binary quadratic forms through what he calls the ‘cubes of integers’. The goal of this article is to introduce the reader to Bhargava’s cubes and this new composition law, as well as to relate it to the composition law as it is known classically.
openaire +1 more source
Class Numbers of Indefinite Binary Quadratic Forms
Journal of Mathematical Sciences, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Factoring with Binary Quadratic Forms
1989In the opening paragraphs of Article 329 of the Disquisitiones, Gauss, a master at calculating, writes [pp. 396–397], The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic ...
openaire +1 more source
Positive Definite Binary Quadratic Forms
2007Abstract A significant portion of Gauss’s Disquitiones Arithmeticae is about binary quadratic forms. Since then there have been numerous treatments, especially for the positive definite case. The most relevant reference for us will be Cox’s book [26]. Also many of the routines described here have built-in versions in PARI.
openaire +1 more source
American Cancer Society nutrition and physical activity guideline for cancer survivors
Ca-A Cancer Journal for Clinicians, 2022Cheryl L Rock +2 more
exaly