Refined Upper Bounds for $L(1,χ)$

Fuente: arXiv

Enregistré dans:

Détails bibliographiques
Auteur principal:	Ezearn, Jeffery
Format:	Preprint
Publié:	2025
Sujets:	Number Theory 11M20
Accès en ligne:	Acceder al recurso
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

Documents similaires

Zeros near $s=1$ and the constant term of $L'/L$ for $L$-functions in the Selberg class
par: Táfula, Christian
Publié: (2020)

Uniform effective estimates for $\vert L(1,χ)\vert$
par: Languasco, Alessandro, et autres
Publié: (2020)

On the distribution of $\log |L(σ, χ)|$ and $\log L(σ, χ_D)$ in the modulus aspect
par: Hosoi, Manami, et autres
Publié: (2024)

Non-vanishing of Dirichlet $L$-functions at the Central Point
par: Qin, Xinhua, et autres
Publié: (2025)

Small values of $| L^\prime/L(1,χ) |$
par: Lamzouri, Youness, et autres
Publié: (2020)

Asymmetric Distribution of Extreme Values of Cubic $L$-functions at $s=1$
par: Darbar, Pranendu, et autres
Publié: (2023)

Upper Bounds for the Lowest First Zero in Families of Cuspidal Newforms
par: Tang, Xueyiming, et autres
Publié: (2024)

Effective Brauer-Siegel theorems for Artin $L$-functions
par: Cho, Peter J., et autres
Publié: (2025)

Explicit Deuring-Heilbronn phenomenon for Dirichlet $L$-functions
par: Benli, Kübra, et autres
Publié: (2024)

Joint extreme values of Dirichlet (L)-functions and their logarithmic derivatives
par: Zhao, Shengbo
Publié: (2026)

On optimality of mollifiers
par: Čech, Martin, et autres
Publié: (2025)

Moments of $L$-functions Problem List
par: Hamieh, Alia, et autres
Publié: (2024)

A variant of the Linnik-Sprindzuk theorem for simple zeros of Dirichlet L-functions
par: Banks, William D.
Publié: (2024)

Upper bounds on gaps between zeros of $L$-functions
par: Zhao, Tianyu
Publié: (2025)

Effective Upper Bound Estimates for $|ζ'(1/2+it)|$ via Exponential Sums
par: Liu, Ting, et autres
Publié: (2025)

Non-vanishing of Dirichlet $L$-functions with smooth conductors
par: Leung, Sun-Kai
Publié: (2024)

Numerical Computations Concerning Landau-Siegel Zeros
par: Lu, Rick F., et autres
Publié: (2026)

Littlewood's estimates for $L$-functions in the hyperelliptic ensemble
par: Carneiro, Emanuel, et autres
Publié: (2025)

Paratrophic Determinants over $\mathbb{Z}/N\mathbb{Z}$ via Discrete Fourier Transform
par: Liu, Hang
Publié: (2026)

Upper bounds for moments of Dirichlet $L$-functions to a fixed modulus
par: Gao, Peng, et autres
Publié: (2025)

Non-Vanishing of Dirichlet $L$-functions at the central point with restricted root number
par: Earnst, Adam
Publié: (2026)

Numerical estimates on the Landau-Siegel zero and other related quantities
par: Languasco, Alessandro
Publié: (2023)

Large values of quadratic Dirichlet $L$-functions
par: Darbar, Pranendu, et autres
Publié: (2024)

Multitangent functions and symmetric multiple zeta values
par: Hirose, Minoru
Publié: (2024)

On the Frobenius Problem for Some Generalized Fibonacci Subsequences -- II
par: Shaikh, Ryan Azim, et autres
Publié: (2025)

On the Frobenius Problem for Some Generalized Fibonacci Subsequences -- I
par: Panda, Santak, et autres
Publié: (2024)

On numerical semigroups with embedding dimension four
par: Chomicz, Kazimierz
Publié: (2026)

Bounds for Moments of Dirichlet $L$-functions of fixed modulus on the critical line
par: Gao, Peng, et autres
Publié: (2025)

Pointwise and correlation bounds on Dedekind sums over small subgroups
par: Borda, Bence, et autres
Publié: (2023)

The $L$-polynomial of hyperelliptic function fields and its applications
par: Cho, Peter Jaehyun, et autres
Publié: (2025)

Explicit Lower Bounds for Dirichlet Series of Higher Power Representation Functions
par: Gurram, Mahipal
Publié: (2025)

The Frobenius number corresponding to the squares of three consecutive Fibonacci numbers: comparison of three algorithmic processes
par: Robles-Pérez, Aureliano M., et autres
Publié: (2025)

Newman's conjecture, zeros of the L-functions, function fields
par: Chang, Alan, et autres
Publié: (2014)

Reciprocity For Dedekind Sums via Conical Zeta Values
par: Torres-Nova, Yerko
Publié: (2025)

On Landau-Siegel zeros and heights of singular moduli
par: Táfula, Christian
Publié: (2019)

On a certain identity for the cotangent zeta finite Dirichlet series and its application to the Berndt--Arakawa formula
par: Furusawa, Masaaki, et autres
Publié: (2024)

Comparative Prime Number Theory Problem List
par: Hamieh, Alia, et autres
Publié: (2024)

Egyptian fractions for few primes
par: Czenky, Agustina, et autres
Publié: (2025)

Analytic properties of representation zeta functions of groups of type $\mathsf{A_2}$
par: Blomer, Valentin, et autres
Publié: (2025)

Upper bounds for shifted moments of quadratic Dirichlet $L$-functions over function fields
par: Gao, Peng, et autres
Publié: (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
language	"fr"
VUFIND_SESSION	"899adf88e736f4f98863dd6921ae7a48"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790968876.17 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "899adf88e736f4f98863dd6921ae7a48" ]`]
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	"language=fr; VUFIND_SESSION=899adf88e736f4f98863dd6921ae7a48; ui=standard"
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	"37654"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2503_06210/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2503_06210/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790968876.1523
REQUEST_TIME	1790968876

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler