Secondary terms in the first moment of $|{\rm Sel}_2(E)|$

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Shankar, Arul, Taniguchi, Takashi
Format:	Preprint
Published:	2024
Subjects:	Number Theory
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Secondary terms in the counting functions of quartic fields II
by: Shankar, Arul, et al.
Published: (2025)

Malle's Conjecture for Galois octic fields over $\mathbb Q$
by: Shankar, Arul, et al.
Published: (2025)

On the asymptotics of cubic fields ordered by general invariants
by: Shankar, Arul, et al.
Published: (2022)

Finiteness theorems for some representations of $\mathrm{GL}_3$
by: Janbazi, Fatemehzahra, et al.
Published: (2025)

The second moment of the size of the $2$-class group of monogenized cubic fields
by: Bhargava, Manjul, et al.
Published: (2025)

Squarefree values of polynomial discriminants II
by: Bhargava, Manjul, et al.
Published: (2022)

Mixed moments of $\rm GL(2)$ and symmetric square $L$-functions
by: Huang, Bingrong, et al.
Published: (2024)

Counting integral points on symmetric varieties with applications to arithmetic statistics
by: Shankar, Arul, et al.
Published: (2023)

Uniform Integrality of critical values of the Rankin-Selberg $L$-function for ${\rm GL}_{n}\times {\rm GL}_{n-1}$
by: Hara, Takashi, et al.
Published: (2023)

Geometry-of-numbers methods over global fields II: Coregular representations
by: Bhargava, Manjul, et al.
Published: (2026)

Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces
by: Bhargava, Manjul, et al.
Published: (2015)

On gamma factors of generic representations of ${\rm U}_{2n+1}\times{\rm Res}_{E/F}{\rm GL}_r$
by: Cheng, Yao, et al.
Published: (2023)

On the error term in a mixed moment of L-functions
by: Khan, Rizwanur, et al.
Published: (2024)

The existence of infinitely many cubic fields with class group of exact 2-rank 1
by: Bhargava, Manjul, et al.
Published: (2026)

On moments of the error term of the multivariable k-th divisor functions
by: Guo, Zhen, et al.
Published: (2024)

Spectral Reciprocity for the first moment of triple product $L$-functions and applications
by: Miao, Xinchen
Published: (2024)

The first moment of central value of primitive quartic $L$-functions with fixed genus
by: Hong, Ziwei
Published: (2025)

Hybrid subconvexity bounds for twists of $\rm GL_2\times\rm GL_2$ $L$-functions
by: Shao, Chenchen, et al.
Published: (2025)

On high power moments of the error term of the Dirichlet divisor function over primes
by: Guo, Zhen, et al.
Published: (2024)

First moments of ${\rm{GL}} (3) \times {\rm{GL}} (2)$ and ${\rm{GL}} (2)$ $L$-functions and their applications
by: Hou, Fei
Published: (2025)

$p$-adic $L$-functions for ${\rm GSp}(4)\times {\rm GL}(2)$ II
by: Liu, Zheng
Published: (2024)

Uniform bounds for lattice point counting and partial sums of zeta functions
by: Lowry-Duda, David, et al.
Published: (2017)

On the higher moments of the error term in the Rankin-Selberg problem
by: Huang, Jing, et al.
Published: (2025)

On the error term of the fourth moment of the Riemann zeta-function
by: Palojärvi, Neea, et al.
Published: (2025)

Base change and Iwasawa Main Conjectures for ${\rm GL}_2$
by: Burungale, Ashay, et al.
Published: (2024)

Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
by: Shankar, Ananth N., et al.
Published: (2019)

Exponential sums over singular binary quartic forms and applications
by: Ishitsuka, Yasuhiro, et al.
Published: (2024)

Counting number fields of fixed degree by their smallest defining polynomial
by: Arango-Piñeros, Santiago, et al.
Published: (2026)

Mixed fourth moments of automorphic forms and the shifted moments of $L$-functions
by: Guo, Chengliang
Published: (2026)

Subconvexity for $\rm GL_2 \times GL_2$ $L$-functions in the depth aspect
by: Zhu, Tengyou
Published: (2025)

Secondary terms in the distribution of genus numbers of cubic fields
by: Yamada, Tatsuya
Published: (2026)

Remarks on the disproof of the unit distance conjecture
by: Alon, Noga, et al.
Published: (2026)

The second moment of Ramanujan sums
by: Ziwei, Hong, et al.
Published: (2025)

Odd moments and adding fractions
by: Bloom, Thomas F., et al.
Published: (2023)

Odd moments in the distribution of primes
by: Kuperberg, Vivian
Published: (2021)

Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness
by: Cheng, Yao
Published: (2025)

Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Reduction
by: Cheng, Yao
Published: (2026)

Whittaker functions on ${\rm GL}_n$ via theta lifting
by: Chen, Shih-Yu, et al.
Published: (2026)

Upper bounds for moments of zeta sums
by: Gao, Peng
Published: (2024)

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"
language	"en"
VUFIND_SESSION	"2f7494224b0dfdefbf0a6da1fed2f510"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790951342.8166 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "2f7494224b0dfdefbf0a6da1fed2f510" ]`]
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; language=en; VUFIND_SESSION=2f7494224b0dfdefbf0a6da1fed2f510"
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	"12316"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2412_00995/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2412_00995/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790951342.8084
REQUEST_TIME	1790951342

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"2f7494224b0dfdefbf0a6da1fed2f510"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790951342.8166 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "2f7494224b0dfdefbf0a6da1fed2f510" ]`]
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; language=en; VUFIND_SESSION=2f7494224b0dfdefbf0a6da1fed2f510"
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	"12316"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2412_00995/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2412_00995/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790951342.8084
REQUEST_TIME	1790951342

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: