The prime number theorem and pair correlation of zeros of the Riemann zeta-function

We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery’s conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in long ranges and with suitable error terms.

Uloženo v:
Podrobná bibliografie
Vydáno v:Research in number theory Ročník 8; číslo 4
Hlavní autoři: Goldston, D. A., Suriajaya, Ade Irma
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.12.2022
Springer Nature B.V
Témata:
Mathematics
Mathematics and Statistics
Number Theory
Prime numbers
Theorems
11M26
Prime numbers
11M06
11N05
Riemann zeta-function
Prime number theorem
ISSN:2522-0160, 2363-9555
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery’s conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in long ranges and with suitable error terms.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-022-00371-4