THE RIEMANN-HYPOTHESIS, VIBRATING FRACTAL STRINGS AND THE MODIFIED WEYL-BERRY CONJECTURE

被引：0

作者：

LAPIDUS, ML

MAIER, H

机构：

[1] YALE UNIV,DEPT MATH,NEW HAVEN,CT 06520

[2] UNIV GEORGIA,BOYD GRAD STUDIES RES CTR,DEPT MATH,ATHENS,GA 30602

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1991年 / 313卷 / 01期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Jointly with C. Pomerance, the first author has recently proved in dimension one the "modified Weyl-Berry conjecture" formulated in his earlier work on the vibrations of fractal drums. Here, we show, in particular, that (still in dimension one) the converse of this conjecture is not true in the "midfractal" case and that it is true everywhere else if and only if the Riemann hypothesis is true. We thus obtain a new characterization of the Riemann hypothesis by means of an inverse spectral problem.

引用

页码：19 / 24

页数：6

共 20 条

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Lapidus, ML
Pomerance, C
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LAPIDUS, ML
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LAPIDUS, ML
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[J]. ACTA MATHEMATICA SINICA-NEW SERIES, 1998, 14 (02): : 261 - 276
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