THE ARITHMETIC AND SPECTRAL ANALYSIS OF POINCARÉ SERIES

By ANTHONY TAYLOR

CONTENTS A SHORT BIOGRAPHY AND THE WORK OF PROFESSOR SUNADA BRIEF PRO?LE OF PROFESSOR TOSHIKAZU SUNADA AN OVERVIEW OF SUNADA’S WORK UP TO AGE ARTICLES SUNADA’S ISOSPECTRALITY TECHNIQUE: TWO DECADES LATER A CENTRAL LIMIT THEOREM ON MODI?ED GRAPHS OF NILPOTENT COVERING GRAPHS HIDDEN SYMMETRIES AND SPECTRUM OF THE LAPLACIAN ON AN INDE?NITE RIEMANNIAN MANIFOLD SPECTRA OF ALTERNATING HILBERT OPERATORS A LIOUVILLE PROPERTY AND ITS APPLICATION TO THE LAPLACIAN OF AN IN?NITE GRAPH A NOTE ON ZERO-FREE REGIONS FOR THE DERIVATIVE OF SELBERG ZETA FUNCTIONS CHERN-SIMONS VARIATION AND DELIGNE COHOMOLOGY RENORMALIZED RAUZY-VEECH-ZORICH INDUCTIONS VISUALIZATION OF STANDARD REALIZED CRYSTAL LATTICES VALUE DISTRIBUTION AND DISTRIBUTION OF RATIONAL POINTS LIMITING DISTRIBUTIONS FOR GEODESICS EXCURSIONS ON THE MODULAR SURFACE ON THE STATISTICS OF THE MINIMAL SOLUTION OF A LINEAR DIOPHANTINE EQUATION AND UNIFORM DISTRIBUTION OF THE REAL PART OF ORBITS IN HYPERBOLIC SPACES ´ COMPUTATIONS OF SPECTRAL RADII ON G-SPACES LENGTHS, QUASI-MORPHISMS AND STATISTICS FOR FREE GROUPS SEMICLASSICAL ASYMPTOTICS ON MANIFOLDS WITH BOUNDARY ON GEOMETRIC ANALOGUES OF THE BIRCH AND SWINNERTON-DYER CONJECTURE FOR LOW DIMENSIONAL HYPERBOLIC MANIFOLDS RAY-SINGER ZETA FUNCTIONS FOR COMPACT FLAT MANIFOLDS BERNSTEIN MEASURES ON CONVEX POLYTOPES REAL AND COMPLEX ZEROS OF RIEMANNIAN RANDOM WAVES