Modular Symbols have a Normal Distribution

By Y. Petridis, Morten S. Risager. 2003

58 citations recorded by the source corpus.

Abstract.We prove that the modular symbols appropriately normalized and ordered have a Gaussian distribution for all cofinite subgroups of % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4uaiaabY % eadaWgaaWcbaGaaeOmaaqabaGccaGGOaWefv3ySLgznfgDOjdaryqr % 1ngBPrginfgDObcv39gaiuaacqWFDeIucaGGPaGaaiOlaaaa!4541! $${\text{SL}}_{\text{2}} (\mathbb{R}).$$ We use spectral deformations to study the poles and the residues of Eisenstein series twisted by power of modular symbols.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/975b09e79336cc0d755e3a4bad15213f5c09e10d