A weighted one-level density of families of L-functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489707" target="_blank" >RIV/00216208:11320/24:10489707 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Qompg9D8Bw" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Qompg9D8Bw</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2140/ant.2024.18.87" target="_blank" >10.2140/ant.2024.18.87</a>

Result language
angličtina
Original language name
A weighted one-level density of families of L-functions
Original language description
This paper is devoted to a weighted version of the one-level density of the nontrivial zeros of L-functions, tilted by a power of the L-function evaluated at the central point. Assuming the Riemann hypothesis and the ratio conjecture, for some specific families of L-functions, we prove that the same structure suggested by the density conjecture also holds in this weighted investigation, if the exponent of the weight is small enough. Moreover, we speculate about the general case, conjecturing explicit formulae for the weighted kernels.
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/GM21-00420M" target="_blank" >GM21-00420M: Universal Quadratic Forms and Class Numbers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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