TY - BOOK

T1 - Studies in the Hyperbolic Circle Problem

AU - Cherubini, Giacomo

PY - 2016

Y1 - 2016

N2 - In this thesis we study the remainder term e(s) in the hyperbolic lattice pointcounting problem. Our main approach to this problem is that of the spectraltheory of automorphic forms. We show that the function e(s) exhibits propertiessimilar to those of almost periodic functions, and we study dierent aspects ofthe theory of almost periodic functions, namely criteria for the existence ofasymptotic moments and limiting distribution for such type of functions. Thisgives us the possibility to infer nontrivial bounds on higher moments of e(s), andexistence of asymptotic moments and limiting distribution for certain integralversions of it. Finally we describe what results can be obtained by applicationof fractional calculus, especially fractional integration to small order, to theproblem.

AB - In this thesis we study the remainder term e(s) in the hyperbolic lattice pointcounting problem. Our main approach to this problem is that of the spectraltheory of automorphic forms. We show that the function e(s) exhibits propertiessimilar to those of almost periodic functions, and we study dierent aspects ofthe theory of almost periodic functions, namely criteria for the existence ofasymptotic moments and limiting distribution for such type of functions. Thisgives us the possibility to infer nontrivial bounds on higher moments of e(s), andexistence of asymptotic moments and limiting distribution for certain integralversions of it. Finally we describe what results can be obtained by applicationof fractional calculus, especially fractional integration to small order, to theproblem.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122190857005763

M3 - Ph.D. thesis

BT - Studies in the Hyperbolic Circle Problem

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -