Motivated by the list of problems for moments of $L$-functions due to Hamieh et al. [7], we prove an asymptotic formula for the cubic moment of central $L$-values associated to holomorphic cusp forms of level one, where the weights $k$ lie in a short interval $K-\Delta <k<K+\Delta $ with $K^\varepsilon \le \Delta \le K^{1-\varepsilon }$, as $K\rightarrow \infty $.
Motivés par la liste des problèmes concernant les moments des fonctions $L$ établie par Hamieh et al. [7], nous démontrons une formule asymptotique pour le moment cubique des valeurs centrales des fonctions $L$ associées aux formes modulaires paraboliques holomorphes de niveau un, où les poids $k$ varient dans un court intervalle $K-\Delta <k<K+\Delta $ avec $K^\varepsilon \le \Delta \le K^{1-\varepsilon }$, lorsque $K \rightarrow \infty $.
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Keywords: Cubic moment, the moment conjecture, Petersson trace formula
Hui Wang 1 ; Xin Wang 2
CC-BY-ND 4.0
Hui Wang; Xin Wang. The cubic moment of central $L$-values in the weight aspect. Journal de théorie des nombres de Bordeaux, Tome 38 (2026) no. 2, pp. 533-556. doi: 10.5802/jtnb.1372
@article{JTNB_2026__38_2_533_0,
author = {Hui Wang and Xin Wang},
title = {The cubic moment of central $L$-values in the weight aspect},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {533--556},
year = {2026},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {38},
number = {2},
doi = {10.5802/jtnb.1372},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1372/}
}
TY - JOUR AU - Hui Wang AU - Xin Wang TI - The cubic moment of central $L$-values in the weight aspect JO - Journal de théorie des nombres de Bordeaux PY - 2026 SP - 533 EP - 556 VL - 38 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1372/ DO - 10.5802/jtnb.1372 LA - en ID - JTNB_2026__38_2_533_0 ER -
%0 Journal Article %A Hui Wang %A Xin Wang %T The cubic moment of central $L$-values in the weight aspect %J Journal de théorie des nombres de Bordeaux %D 2026 %P 533-556 %V 38 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1372/ %R 10.5802/jtnb.1372 %G en %F JTNB_2026__38_2_533_0
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