A new proof of Halász’s theorem, and its consequences

DOI10.1112/S0010437X18007522zbMath1443.11200arXiv1706.03749OpenAlexW2626951099WikidataQ102399496 ScholiaQ102399496MaRDI QIDQ5227654

Andrew Granville, Adam J. Harper, Kannan Soundararajan

Publication date: 7 August 2019

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03749

zbMATH Keywords

multiplicative functionsHalász's theoremLinnik's theoremSiegel zeroesHoheisel's theorem

Mathematics Subject Classification ID

Real zeros of (L(s, chi)); results on (L(1, chi)) (11M20) Rate of growth of arithmetic functions (11N56)

Related Items (14)

Exponential sums with multiplicative coefficients and applications ⋮ A more intuitive proof of a sharp version of Halász’s theorem ⋮ Divisor-bounded multiplicative functions in short intervals ⋮ A pretentious proof of Linnik's estimate for primes in arithmetic progressions ⋮ Multiplicative functions in short arithmetic progressions ⋮ Three conjectures about character sums ⋮ Bombieri-Vinogradov for multiplicative functions, and beyond the \(x^{1/2}\)-barrier ⋮ Correlation of multiplicative functions over Fq[x$\mathbb {F}_q[x]$: A pretentious approach] ⋮ Mean values of multiplicative functions over function fields ⋮ SMOOTH‐SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE ‐BARRIER ⋮ A note on Halász's theorem in \(\mathbb{F}_q[t\)] ⋮ Zeros of Dirichlet polynomials ⋮ Zeros of partial sums of \(L\)-functions ⋮ The structure of multiplicative functions with small partial sums

Cites Work

• Weak subconvexity for central values of \(L\)-functions
• Mean values of multiplicative functions over function fields
• Pretentious multiplicative functions and the prime number theorem for arithmetic progressions
• Multiplicative Functions on Arithmetic Progressions. VII: Large Moduli
• A more intuitive proof of a sharp version of Halász’s theorem
• A Brun-Titschmarsh theorem for multiplicative functions.
• Decay of Mean Values of Multiplicative Functions
• Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen
• Mean values of multiplicative functions
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