The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures

Terence Tao, Joni Teräväinen

Type: Article

Publication Date: 2019-07-23

Citations: 60

DOI: https://doi.org/10.1215/00127094-2019-0002

View Publication

Download PDF

Abstract

Let g 0

Locations

Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF
Oxford University Research Archive (ORA) (University of Oxford) - View - PDF
DataCite API - View
Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF
Oxford University Research Archive (ORA) (University of Oxford) - View - PDF
DataCite API - View
Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF
Oxford University Research Archive (ORA) (University of Oxford) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Properties of exponentials and logarithmic functions	2012	Marc R. Roussel
+	Finite and infinite series of G-functions	1973	A. M. Mathai R. K. Saxena
+	Exponential sums	1991
+	Exponential sums with multiplicative coefficients	1989	K.‐H. Indlekofer И. Катаи
+ PDF	Exponential sums with multiplicative coefficients	1977	Hugh L. Montgomery R. C. Vaughan
+	L-functions of exponential sums and Hasse polynomials	2021	Wei Cao
+ PDF	Freud’s conjecture for exponential weights	1986	D. S. Lubinsky H. N. Mhaskar Edward B. Saff
+	Exponential sums and the Riemann conjecture	1973	P. Túrán
+ PDF	Lambert series, false theta functions, and partitions	1972	George E. Andrews
+	Logarithmic Operators and Characterizations of Completely Multiplicative Functions	2001	Vichian Laohakosol Nittiya Pabhapote Nalinee Wechwiriyakul
+	Logarithmic Operators and Characterizations of Completely Multiplicative Functions	2001	Vichian Laohakosol Nittiya Pabhapote Nalinee Wechwiriyakul
+	Exact Statistics and Continued Fractions	1996	David Lester
+	Correlation in E(∞)	2000	Μ.S. El Naschie
+	Multiplicative Functions	2003	Svetoslav Savchev Titu Andreescu
+	Sums of logarithmic weights involving r-full numbers	2024	Isao Kiuchi
+	𝑞-Series with Applications to Combinatorics, Number Theory, and Physics	2001	Bruce C. Berndt Ken Ono
+	Exponential sums: the estimate of Hasse-Davenport-Weil	1998	Peter Roquette
+	Necklace rings and logarithmic functions	2005	Young-Tak Oh
+	Major Index Statistics: Cyclic Sieving, Branching Rules, and Asymptotics	2018	Joshua P. Swanson
+	The Bruhat order and iterated exponentials	1989	John R. Stembridge

Works That Cite This (61)

Action	Title	Year	Authors
+	Möbius disjointness for nilsequences along short intervals	2020	Xiaoguang He Zhiren Wang
+ PDF	Dynamical models for Liouville and obstructions to further progress on sign patterns	2020	Will Sawin
+	Structure of multicorrelation sequences with integer part polynomial iterates along primes	2020	Andreas Koutsogiannis Anh Lê Joel Moreira Florian Richter
+ PDF Chat	Gowers norms control diophantine inequalities	2020	Aled Walker
+ PDF	Divisor-bounded multiplicative functions in short intervals	2023	Alexander P. Mangerel
+ PDF Chat	Polynomial mean complexity and logarithmic Sarnak conjecture	2023	Wen Huang Leiye Xu Xiangdong Ye
+	Sarnak's Conjecture for Sequences of Almost Quadratic Word Growth	2019	Redmond McNamara
+	Siegel Zeros and Sarnak's Conjecture	2021	Jake Chinis
+ PDF	On Furstenberg systems of aperiodic multiplicative functions of Matomäki, Radziwiłł, and Tao	2021	Aleksander Gomilko Mariusz Lemańczyk Thierry de La Rue
+	Sarnak's Conjecture for nilsequences on arbitrary number fields and applications	2019	Wenbo Sun

Works Cited by This (41)

Action	Title	Year	Authors
+ PDF	An averaged form of Chowla’s conjecture	2015	Kaisa Matomäki Maksym Radziwiłł Terence Tao
+	Disjointness of Moebius from Horocycle Flows	2012	Jean Bourgain Peter Sarnak Tamar Ziegler
+ PDF	Exponential sums with multiplicative coefficients	1977	Hugh L. Montgomery R. C. Vaughan
+	NOTE ON AN ASYMPTOTIC FORMULA CONNECTED WITH <i>r</i>-FREE INTEGERS	1947	L. Mirsky
+ PDF	Multiple recurrence and convergence for sequences related to the prime numbers	2007	Nikos Frantzikinakis Bernard Host Bryna Kra
+	On the correlation of multiplicative and the sum of additive arithmetic functions	1994	P. D. T. A. Elliott
+	A remark on a theorem of H. Daboussi	1986	И. Катаи
+	On Multiplicative Arithmetical Functions whose Modulus does not Exceed One	1982	Hédi Daboussi Hubert Delange
+	Das asymptotische Verhalten von Summen über multiplikative Funktionen. II	1967	Eduard Wirsing
+ PDF	Linear equations in primes	2010	Ben Green Terence Tao