On the uniform distribution of the zero ordinates of the $L-$function associated with $θ(z)^{-3}\,η(2z)^{12}$

Fuente: arXiv

Saved in:

Bibliographic Details
Main Author:	Ribeiro, Pedro
Format:	Preprint
Published:	2024
Subjects:	Number Theory
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Shifting the ordinates of zeros of the Riemann zeta function
by: Banks, William D.
Published: (2024)

New zero-free regions for Dedekind zeta-functions at small and large ordinates
by: Das, Sourabhashis, et al.
Published: (2025)

Notes on the multiplier systems of $η(τ)$ and $θ(τ)$
by: Matsuda, Kazuhide
Published: (2025)

Revisiting the equation $x^2+y^3=z^p$
by: Freitas, Nuno, et al.
Published: (2025)

Exceptional zeros of Rankin-Selberg $L$-functions and joint Sato-Tate distributions
by: Thorner, Jesse
Published: (2024)

Simple zeros of $\mathrm{GL}(2)$ $L$-functions
by: de Faveri, Alexandre
Published: (2021)

Bounded Representations by $x^2+y^2-z^2$
by: Chojecki, Przemyslaw
Published: (2026)

Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version)
by: Komatsu, Takao, et al.
Published: (2024)

The $θ$-adics
by: Gendron, T. M., et al.
Published: (2025)

Estimates for the number of zeros of shifted combinations of completed Dirichlet series
by: Ribeiro, Pedro
Published: (2024)

Landau-Siegel zeros of Rankin-Selberg $L$-functions
by: Thorner, Jesse, et al.
Published: (2026)

Exceptional zeros of $\mathrm{GL}_3\times\mathrm{GL}_3$ Rankin-Selberg $L$-functions
by: Thorner, Jesse
Published: (2025)

On the inverse stability of $z^n+c.$
by: Ji, Yang Gao Qingzhong
Published: (2025)

Weighted uniform distribution of subpolynomial functions along primes and applications
by: Bergelson, Vitaly, et al.
Published: (2025)

One-level density of zeros of $Γ_1(q)$ $L$-functions
by: Paul, Arijit
Published: (2025)

Geometric Aspects to Diophantine Equations of the Form $x^2 + zxy + y^2 = M$ and $z$-Rings
by: Busenhart, Chris
Published: (2024)

Non-zero values of a family of approximations of a class of $L$-functions
by: Roy, Arindam, et al.
Published: (2024)

Low-lying zeros of a large orthogonal family of automorphic $L$-functions
by: Baluyot, Siegfred, et al.
Published: (2023)

A connection between low-lying zeros and central values of $L$-functions
by: Lesesvre, Didier, et al.
Published: (2026)

On density of the zeros of Dedekind zeta-functions
by: Zhang, Wei
Published: (2022)

On the vanishing of coefficients of $η^{26}
by: Krishnamoorthy, S., et al.
Published: (2024)

A new Andrews--Crandall-type identity and the number of integer solutions to $x^2+2y^2+2z^2=n$
by: Dospolova, Mariia, et al.
Published: (2023)

On the almost universality of $\lfloor x^2/a\rfloor+\lfloor y^2/b\rfloor+\lfloor z^2/c\rfloor$
by: Wu, Hai-Liang, et al.
Published: (2018)

Detecting zeros of Dirichlet $L$-functions via the Riemann zeta-function
by: Suzuki, Masatoshi
Published: (2025)

Real zeros of $L'(s, χ_d)$
by: Lamzouri, Youness, et al.
Published: (2025)

A note on the zeros of $L$-functions associated to fixed-order Dirichlet characters
by: Corrigan, C. C.
Published: (2023)

Points totalement réels de la courbe $x^5+y^5+z^5=0$
by: Kraus, Alain
Published: (2024)

Counting Square-full Solutions to $x+y=z$
by: Heath-Brown, D. R.
Published: (2026)

On the asymptotic average diameter of blocks of uniformly distributed sequences and related results
by: Heintze, Sebastian, et al.
Published: (2026)

A note on The asymptotic uniform distribution of subset sums
by: Hu, Yilong
Published: (2026)

A metric approach to zero-free regions for $L$-functions
by: Wattanawanichkul, Nawapan
Published: (2025)

Repulsion of zeros close to $s=1/2$ for L-functions
by: Coloma, Nicolás, et al.
Published: (2024)

Multiplicity of nontrivial zeros of primitive L-functions via higher-level correlations
by: Gonçalves, Felipe, et al.
Published: (2023)

Local Fourier uniformity of higher divisor functions on average
by: Wang, Mengdi
Published: (2024)

Circularity in Finite Fields and Solutions of the Equations $\boldsymbol{x^{m}+y^{m}-z^{m}=1}$
by: Ke, Wen-Fong, et al.
Published: (2023)

The $θ= \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$-functions
by: Dong, Anji, et al.
Published: (2026)

An analogue of a formula of Popov II
by: Ribeiro, Pedro
Published: (2026)

A theory for the zeros of Riemann $ζ$ and other $L$-functions (updated)
by: França, Guilherme, et al.
Published: (2014)

An effective Linear Independence conjecture for the zeros of the Riemann zeta function and applications
by: Lamzouri, Youness
Published: (2023)

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	"2d78db941e90c22ca322bd60c2a2e979"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790854401.3212 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "2d78db941e90c22ca322bd60c2a2e979" ]`]
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=2d78db941e90c22ca322bd60c2a2e979"
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	"216.73.216.147"
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	"42306"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2407_14173/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2407_14173/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790854401.3169
REQUEST_TIME	1790854401

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	"2d78db941e90c22ca322bd60c2a2e979"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790854401.3212 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "2d78db941e90c22ca322bd60c2a2e979" ]`]
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=2d78db941e90c22ca322bd60c2a2e979"
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	"216.73.216.147"
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	"42306"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2407_14173/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2407_14173/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790854401.3169
REQUEST_TIME	1790854401

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: