A Refined Conjecture for the Variance of Gaussian Primes across Sectors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472019" target="_blank" >RIV/00216208:11320/23:10472019 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xiVx.vRsnZ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xiVx.vRsnZ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/10586458.2020.1753598" target="_blank" >10.1080/10586458.2020.1753598</a>

Result language
angličtina
Original language name
A Refined Conjecture for the Variance of Gaussian Primes across Sectors
Original language description
We derive a refined conjecture for the variance of Gaussian primes across sectors, with a power saving error term, by applying the L-functions Ratios Conjecture. We observe a bifurcation point in the main term, consistent with the Random Matrix Theory (RMT) heuristic previously proposed by Rudnick and Waxman. Our model also identifies a second bifurcation point, undetected by the RMT model, that emerges upon taking into account lower order terms. For sufficiently small sectors, we moreover prove an unconditional result that is consistent with our conjecture down to lower order terms.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ17-04703Y" target="_blank" >GJ17-04703Y: Quadratic forms and numeration systems over number fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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