Vinogradov’s Mean Value Theorem as an Ingredient in Polynomial Large Sieve Inequalities and Some Consequences

Karin Halupczok ()
Additional contact information
Karin Halupczok: Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf

A chapter in Irregularities in the Distribution of Prime Numbers, 2018, pp 97-109 from Springer

Abstract: Abstract We discuss the role of Vinogradov’s mean value theorem in polynomial large sieve inequalities. We present an application to the distribution of fractions with k-th power denominators. Moreover, polynomial large sieve inequalities lead to a new approach of understanding certain aspects of prime distribution in arithmetic progressions, namely in Bombieri–Vinogradov’s theorem with moduli of special multivariable polynomial shape. The recent progress leading to the main conjecture of Vinogradov’s mean value theorem has an impact to such applications.

Keywords: Large Sieve Inequality; Bombieri Vinogradov; Denominator Power; Multivariable Polynomial; Polynomial Shape (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-92777-0_5

Ordering information: This item can be ordered from
http://www.springer.com/9783319927770

DOI: 10.1007/978-3-319-92777-0_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().