# Spectral Analysis in Geometry and Number Theory

Share this page *Edited by *
*Motoko Kotani; Hisashi Naito; Tatsuya Tate*

This volume is an outgrowth of an international
conference in honor of Toshikazu Sunada on the occasion of his
sixtieth birthday. The conference took place at Nagoya University, Japan, in
2007.

Sunada's research covers a wide spectrum of spectral analysis,
including interactions among geometry, number theory, dynamical
systems, probability theory and mathematical physics. Readers will
find papers on trace formulae, isospectral problems, zeta functions,
quantum ergodicity, random waves, discrete geometric analysis, value
distribution, and semiclassical analysis. This volume also contains
an article that presents an overview of Sunada's work in mathematics
up to the age of sixty.

#### Readership

Graduate students and research mathematicians interested in geometry, number theory, and dynamical systems.

# Table of Contents

## Spectral Analysis in Geometry and Number Theory

- Contents v7 free
- Preface vii9 free
- Acknowledgment ix11 free
- International Conference x12 free
- Program of Conference xi13 free
- A Short Biography and the Work of Professor Sunada 115 free
- Articles 4357
- Sunada's Isospectrality Technique: Two Decades Later 4559
- A Central Limit Theorem on Modified Graphs of Nilpotent Covering Graphs 5973
- Hidden Symmetries and Spectrum of the Laplacian on an Indefinite Riemannian Manifold 7387
- Spectra of Alternating Hilbert Operators 89103
- A Note on Zero-Free Regions for the Derivative of Selberg Zeta Functions 117131
- A Liouville Property and its Application to the Laplacian of an Infinite Graph 103117
- Chern-Simons Variation and Deligne Cohomology 127141
- Renormalized Rauzy-Veech-Zorich Inductions 135149
- Visualization of Standard Realized Crystal Lattices 153167
- Value Distribution and Distribution of Rational Points 165179
- Limiting Distributions for Geodesics Excursions on the Modular Surface 177191
- On the Statistics of the Minimal Solution of a Linear Diophantine Equation and Uniform Distribution of the Real Part of Orbits in Hyperbolic Spaces 187201
- Computations of Spectral Radii on G-Spaces 195209
- Lengths, Quasi-Morphisms and Statistics for Free Groups 219233
- Semiclassical Asymptotics on Manifolds with Boundary 239253
- On Geometric Analogues of the Birch and Swinnerton-Dyer Conjecture for Low Dimensional Hyperbolic Manifolds 267281
- Ray-Singer Zeta Functions for Compact Flat Manifolds 287301
- Bernstein Measures on Convex Polytopes 295309
- Real and Complex Zeros of Riemannian Random Waves 321335