RANDOM WALKS THROUGH THE AREAL MAHLER MEASURE: STEPS IN THE COMPLEX PLANE
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10508574" target="_blank" >RIV/00216208:11320/25:10508574 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jVvfWnlfGz" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jVvfWnlfGz</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/qmath/haaf043" target="_blank" >10.1093/qmath/haaf043</a>
Alternative languages
Result language
angličtina
Original language name
RANDOM WALKS THROUGH THE AREAL MAHLER MEASURE: STEPS IN THE COMPLEX PLANE
Original language description
We study the areal Mahler measure of the two-variable,k -parameter family and prove explicit formulas that demonstrate its relation to the standard Mahler measure of these polynomials. The proofs involve interpreting the areal Mahler measure as a random walk in the complex plane and utilizing the areal analogue of the Zeta Mahler function to arrive at the result. Using similar techniques, we also present formulas for a three-variable family in terms of the standard Mahler measure, along with terms that involve certain hypergeometric functions. For both families, we show that its areal Mahler measure is, up to elementary functions, a linear combination of the normal Mahler measure and the volume of the Deninger cycle of the corresponding family.
Czech name
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Czech description
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Classification
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
Result continuities
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)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Quarterly Journal of Mathematics
ISSN
0033-5606
e-ISSN
1464-3847
Volume of the periodical
76
Issue of the periodical within the volume
4
Country of publishing house
GB - UNITED KINGDOM
Number of pages
39
Pages from-to
1315-1353
UT code for WoS article
001618474000001
EID of the result in the Scopus database
2-s2.0-105024991904