On multiplicatively dependent vectors of polynomial values

Fuente: arXiv

Saved in:

Bibliographic Details
Main Author:	Young, Marley
Format:	Preprint
Published:	2024
Subjects:	Number Theory 11N25, 11C08, 11R04
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Galois module structure of algebraic integers of cyclic cubic fields
by: Aoki, Miho
Published: (2024)

A proof of van der Waerden's Conjecture on random Galois groups of polynomials
by: Bhargava, Manjul
Published: (2024)

Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3
by: Tenenbaum, Gérald, et al.
Published: (2024)

Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants
by: Anderson, Theresa C., et al.
Published: (2021)

Galois module structure of algebraic integers of the simplest cubic field
by: Ogawa, Hajime, et al.
Published: (2023)

Galois groups of reciprocal polynomials II: Twisted reciprocal polynomials
by: Anderson, Theresa C., et al.
Published: (2026)

Polynomial densities and Heilbronn's criterion
by: Hibbler, Alexis, et al.
Published: (2025)

Normal integral bases of Lehmer's cyclic quintic fields
by: Hashimoto, Yu, et al.
Published: (2022)

Counting polynomials with positive roots
by: Yatsyna, Pavlo, et al.
Published: (2025)

Galois groups of reciprocal polynomials and the van der Waerden-Bhargava theorem
by: Anderson, Theresa C., et al.
Published: (2024)

Galois groups of random integer polynomials and van der Waerden's Conjecture
by: Bhargava, Manjul
Published: (2021)

Irreducibility of polynomials with random multiplicative coefficients revisited
by: Klurman, Oleksiy, et al.
Published: (2025)

Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials
by: Gaál, István
Published: (2024)

The $t$-metric Mahler measures of surds and rational numbers
by: Samuels, Charles L., et al.
Published: (2014)

On multiplicative dependence between elements of polynomial orbits
by: Young, Marley
Published: (2024)

On a polynomial involving quadratic residues modulo primes
by: Sun, Zhi-Wei
Published: (2026)

The abc conjecture implies infinitely many non-Wieferich places for fixed bases in number fields
by: Graves, Hester, et al.
Published: (2025)

Irreducibility criteria for pairs of polynomials whose resultant is a prime number
by: Bonciocat, Nicolae Ciprian
Published: (2023)

Calculating generators of power integral bases in sextic fields with a quadratic subfield: the general case
by: Gaál, István
Published: (2025)

Calculating generators of power integral bases in sextic fields with a real quadratic subfield
by: Gaál, István
Published: (2025)

Investigating monogenity in a family of cyclic sextic fields
by: Gaál, István
Published: (2025)

Power integral bases in a family of octic fields
by: Gaál, István
Published: (2025)

Monogenity of pure quintic fields: the power of sieving
by: Gaál, István
Published: (2026)

On vector valued automorphic forms for the Weil representation
by: Stein, Oliver
Published: (2021)

Kitaoka's Conjecture for quadratic fields
by: Kala, Vitezslav, et al.
Published: (2025)

Number Theory in OSCAR
by: Fieker, Claus, et al.
Published: (2024)

The arithmetic of critical values I: equicritical quartic polynomials
by: Naccarato, Francesco
Published: (2024)

A Structure Sheaf for Kirch Topology
by: Borisov, Alexander
Published: (2026)

Universality criterion sets for quadratic forms over number fields
by: Kala, Vitezslav, et al.
Published: (2024)

On Dold condition and fail factor of linear recurrent sequences
by: Rajs, Mateusz
Published: (2025)

On common index divisors and monogenity of certain number fields defined by trinomials of type $x^{2^r}+ax^m+b$
by: Yakkou, Hamid Ben
Published: (2022)

Gaps in binary cyclotomic polynomials
by: Cafure, Antonio, et al.
Published: (2025)

Prime numbers and factorization of polynomials
by: Singh, Jitender
Published: (2024)

On the index of power compositional polynomials
by: Kaur, Sumandeep, et al.
Published: (2024)

Wieferich primes in number fields and the conjectures of Ankeny--Artin--Chowla and Mordell
by: Fellini, Nic, et al.
Published: (2025)

Sizes of Pre-Images of the Minimal Euclidean Function on the Gaussian Integers
by: Graves, Hester
Published: (2026)

A note on the distribution of prime ideals in real quadratic fields
by: Baier, Stephan, et al.
Published: (2023)

Character sums of Division polynomials twisted by multiplicative functions
by: Bhakta, Subham
Published: (2025)

Minimal Mahler Measure in Quartic Galois Number Fields
by: Paudel, Bishnu, et al.
Published: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"aa037c34e35ad88551efb85a88794408"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790899878.9468 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "aa037c34e35ad88551efb85a88794408" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=aa037c34e35ad88551efb85a88794408; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"55714"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2402_13704/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2402_13704/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790899878.9424
REQUEST_TIME	1790899878

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"aa037c34e35ad88551efb85a88794408"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790899878.9468 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "aa037c34e35ad88551efb85a88794408" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=aa037c34e35ad88551efb85a88794408; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"55714"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2402_13704/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2402_13704/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790899878.9424
REQUEST_TIME	1790899878

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: