Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Τύρος Κωνσταντίνος, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών ΕΚΠΑ, (Επιβλέπων)
Δοδός Παντελής, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ,
Μπαρμπάτης Γεράσιμος, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Το πρόβλημα discrepancy του Erdős
Translated title:
The Erdős discrepancy problem
Summary:
In this thesis we focus on the proof of the discrepancy problem of Erdős, given by Terence Tao. We show that for any sequence f (1), f (2). . . taking values in {-1,+1} the
discrepancy of f is infinite. In fact the argument also applies to
sequences f taking values in the unit sphere of a real or complex Hilbert space.The argument uses three ingredients. The first is a Fourier-analytic reduction, which reduces the problem to the case
when f is replaced by a (stochastic) completely multiplicative function g.
The second is a logarithmically averaged version of the Elliott conjecture, established by Terence Tao.
The final ingredient is a further argument which shows unbounded discrepancy in this case.
Main subject category:
Science
Keywords:
discrepancy, multiplicative fuctions
