p-Adic Integral Geometry

被引：3

作者：

Kulkarni, Avinash ^{[1
]}

Lerario, Antonio ^{[2
]}

机构：

[1] Dartmouth Coll, Math, Hanover, NH 03755 USA

[2] SISSA, Math, I-34136 Trieste, Italy

来源：

SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY | 2021年 / 5卷 / 01期

关键词：

integral geometry formula; p-adic volume; zeros of random polynomials; THEOREM; ZEROS;

D O I：

10.1137/19M1284737

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a p-adic version of the integral geometry formula for averaging the intersection of two p-adic projective varieties. We apply this result to give bounds on the number of points in the modulo pm reduction of a projective variety (reproving a result by Oesterle) and to the study of random p-adic polynomial systems of equations.

引用

页码：28 / 59

页数：32

共 50 条

[31] Contracted Ideals of p-adic Integral Group Rings
Lee, Joongul
TOKYO JOURNAL OF MATHEMATICS, 2020, 43 (02) : 529 - 536
[32] An invariant p-adic q-integral on Zp
Kim, Taekyun
APPLIED MATHEMATICS LETTERS, 2008, 21 (02) : 105 - 108
[33] Noetherianity and privilege in p-adic analytic geometry.
Poineau, Jerome
COMPTES RENDUS MATHEMATIQUE, 2006, 343 (04) : 267 - 270
[34] An invariant p-adic integral associated with Daehee numbers
Kim, T
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2002, 13 (01) : 65 - 69
[35] FIELD OF CONSTANTS OF AN INTEGRAL DERIVATION ON A P-ADIC FIELD
THWING, HW
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (07): : 1048 - &
[36] p-Adic Pseudodifferential Operators and p-Adic Wavelets
S. V. Kozyrev
Theoretical and Mathematical Physics, 2004, 138 : 322 - 332
[37] P-ADIC THETA SERIES WITH INTEGRAL-COEFFICIENTS
CRISTANTE, V
ASTERISQUE, 1984, (119-) : 169 - 182
[38] The Geometry of p-Adic Fractal Strings: A Comparative Survey
Lapidus, Michel L.
Hung, Lu
ADVANCES IN NON-ARCHIMEDEAN ANALYSIS, 2011, 551 : 163 - +
[39] Conjectures about p-adic groups and their noncommutative geometry
Aubert, Anne-Marie
Baum, Paul
Plymen, Roger
Solleveld, Maarten
AROUND LANGLANDS CORRESPONDENCES, 2017, 691 : 15 - 51
[40] FIELDS OF CONSTANTS OF INTEGRAL DERIVATIONS ON A P-ADIC FIELD
THWING, HW
HEEREMA, N
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 195 (AUG) : 277 - 290

← 1 2 3 4 5 →