The lattice point discrepancy of a body of revolution:: Improving the lower bound by Soundararajan's method

被引：3

作者：

Kühleitner, M ^{[1
]}

Nowak, WG ^{[1
]}

机构：

[1] Univ Bodenkultur Wien, Dept Integrat Biol, Inst Math, A-1190 Vienna, Austria

来源：

ARCHIV DER MATHEMATIK | 2004年 / 83卷 / 03期

关键词：

D O I：

10.1007/s00013-004-1013-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a convex body B in R-3 which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy P-B(t) (number of integer points minus volume) of a linearly dilated copy roottB is estimated from below. On the basis of a recent method of K. Soundararajan [16], an Omega-bound is obtained that improves upon all earlier results of this kind.

引用

页码：208 / 216

页数：9

共 35 条

[1] The lattice point discrepancy of a body of revolution: Improving the lower bound by Soundararajan’s method
Manfred Kühleitner
Werner Georg Nowak
[J]. Archiv der Mathematik, 2004, 83 : 208 - 216
[2] The Piltz divisor problem in number fields:: An improved lower bound by Soundararajan's method
Girstmair, K
Kühleitner, M
Müller, W
Nowak, WG
[J]. ACTA ARITHMETICA, 2005, 117 (02) : 187 - 206
[3] A lower bound for the discrepancy of a random point set
Doerr, Benjamin
[J]. JOURNAL OF COMPLEXITY, 2014, 30 (01) : 16 - 20
[4] On the lower bound of the discrepancy of Halton’s sequence II
Levin M.B.
[J]. European Journal of Mathematics, 2016, 2 (3) : 874 - 885
[5] On the lower bound of the discrepancy of Halton's sequence I
Levin, Mordechay B.
[J]. COMPTES RENDUS MATHEMATIQUE, 2016, 354 (05) : 445 - 448
[6] On the lower bound of the discrepancy of (t, s) sequences: I
Levin, Mordechay B.
[J]. COMPTES RENDUS MATHEMATIQUE, 2016, 354 (06) : 562 - 565
[7] On the Lower Bound in the Lattice Point Remainder Problem for a Parallelepiped
Levin, Mordechay B.
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2015, 54 (04) : 826 - 870
[8] On the Lower Bound in the Lattice Point Remainder Problem for a Parallelepiped
Mordechay B. Levin
[J]. Discrete & Computational Geometry, 2015, 54 : 826 - 870
[9] LOWER BOUND METHOD FOR LIMIT ANALYSIS OF SHELLS OF REVOLUTION
NAKANISHI, H
SUZUKI, M
HAMADA, M
[J]. JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1975, 42 (02): : 494 - 495
[10] Improving the discrepancy bound for sparse matrices: Better approximations for sparse lattice approximation problems
Srinivasan, A
[J]. PROCEEDINGS OF THE EIGHTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 1997, : 692 - 701

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