|
|||||
 |
|
|
|
|
|
|
|
Generalized Fourier
coefficients of multiplicative functions
Lilian Matthiesen |
|
Vol. 12 (2018), No. 6, 1311–1400
|
Abstract |
|
We introduce and analyze a general class of not necessarily bounded multiplicative functions, examples of which include the function , where and where counts the number of distinct prime factors of , as well as the function , where denotes the Fourier coefficients of a primitive holomorphic cusp form. For this class of functions we show that after applying a -trick, their elements become orthogonal to polynomial nilsequences. The resulting functions therefore have small uniformity norms of all orders by the Green–Tao–Ziegler inverse theorem, a consequence that will be used in a separate paper in order to asymptotically evaluate linear correlations of multiplicative functions from our class. Our result generalizes work of Green and Tao on the Möbius function. |
PDF Access Denied
We have not been able to recognize your IP address
34.239.173.144
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
multiplicative functions, nilsequences, Gowers uniformity
norms
|
Mathematical Subject Classification 2010
Primary: 11B30
Secondary: 11L07, 11N60, 37A45
|
Milestones
Received: 4 July 2016
Revised: 18 September 2017
Accepted: 30 October 2017
Published: 6 October 2018
|
Authors |
| Lilian Matthiesen | |
| Department of Mathematics KTH Stockholm Sweden |
|
