Book Section records
https://feeds.library.caltech.edu/people/Radziwiłł-M/book_section.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:10:05 +0000A Note on Helson's Conjecture on Moments of Random Multiplicative Functions
https://resolver.caltech.edu/CaltechAUTHORS:20180612-151835443
Authors: {'items': [{'id': 'Harper-A-J', 'name': {'family': 'Harper', 'given': 'Adam J.'}}, {'id': 'Nikeghbali-A', 'name': {'family': 'Nikeghbali', 'given': 'Ashkan'}}, {'id': 'Radziwiłł-M', 'name': {'family': 'Radziwiłł', 'given': 'Maksym'}}]}
Year: 2015
DOI: 10.1007/978-3-319-22240-0_11
In this note we are interested in cancellations in sums of multiplicative functions. It is well known that M(x) := Σ n≤x µ(n) = 0(x^(1/2+ε) is equivalent to the Riemann Hypothesis. On the other hand, it is also a classical result that M(x) > x^(1/2+ε) for a sequence of arbitrarily large x. It is in fact conjectured that lim x→ ∞ M(x)/ √x(log log log x)^(5/4) = ±B for some constant B > 0 (see [21]).https://authors.library.caltech.edu/records/38p2e-9qd44