We establish asymptotic formulas for volumes of height balls in analytic varieties over local fields and in adelic points of algebraic varieties over number fields, relating the Mellin transforms of height functions to Igusa integrals and to global geometric invariants of the underlying variety. In the adelic setting, this involves the construction of general Tamagawa measures.
@article{CML_2010__2_3_351_0,
author = {Chambert-Loir, Antoine and Tschinkel, Yuri},
title = {Igusa integrals and volume asymptotics in analytic and adelic geometry},
journal = {Confluentes Mathematici},
pages = {351--429},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {2},
number = {3},
year = {2010},
doi = {10.1142/S1793744210000223},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S1793744210000223/}
}
TY - JOUR AU - Chambert-Loir, Antoine AU - Tschinkel, Yuri TI - Igusa integrals and volume asymptotics in analytic and adelic geometry JO - Confluentes Mathematici PY - 2010 SP - 351 EP - 429 VL - 2 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S1793744210000223/ DO - 10.1142/S1793744210000223 LA - en ID - CML_2010__2_3_351_0 ER -
%0 Journal Article %A Chambert-Loir, Antoine %A Tschinkel, Yuri %T Igusa integrals and volume asymptotics in analytic and adelic geometry %J Confluentes Mathematici %D 2010 %P 351-429 %V 2 %N 3 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S1793744210000223/ %R 10.1142/S1793744210000223 %G en %F CML_2010__2_3_351_0
Chambert-Loir, Antoine; Tschinkel, Yuri. Igusa integrals and volume asymptotics in analytic and adelic geometry. Confluentes Mathematici, Tome 2 (2010) no. 3, pp. 351-429. doi : 10.1142/S1793744210000223. http://www.numdam.org/articles/10.1142/S1793744210000223/
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