The mean-value of a product of shifted multiplicative functions and the average number of points of elliptic curves

R. Balasubramanian, Sumit Giri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the mean value of the product of two real valued multiplicative functions with shifted arguments. The functions F and G under consideration are close to two nicely behaved functions A and B, such that the average value of A(. n-. h). B(. n) over any arithmetic progression is only dependent on the common difference of the progression. We use this method on the problem of finding mean value of NK(. N)/ϕ(. N), where NK(. N)/ϕ(. N)log N is the expected number of primes such that a random elliptic curve over rationals has N points when reduced over those primes.

Original languageEnglish
Pages (from-to)37-53
Number of pages17
JournalJournal of Number Theory
Volume157
DOIs
StatePublished - 1 Dec 2015
Externally publishedYes

Keywords

  • Asymptotic of mean value
  • Elliptic curve over finite fields
  • Shifted multiplicative function

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