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

In: Irregularities in the Distribution of Prime Numbers

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  • Karin Halupczok

    (Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf)

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.

Suggested Citation

  • Karin Halupczok, 2018. "Vinogradov’s Mean Value Theorem as an Ingredient in Polynomial Large Sieve Inequalities and Some Consequences," Springer Books, in: János Pintz & Michael Th. Rassias (ed.), Irregularities in the Distribution of Prime Numbers, pages 97-109, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-92777-0_5
    DOI: 10.1007/978-3-319-92777-0_5
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