TY - JOUR

T1 - The mean-value of a product of shifted multiplicative functions and the average number of points of elliptic curves

AU - Balasubramanian, R.

AU - Giri, Sumit

N1 - Publisher Copyright:
© 2015 Elsevier Inc.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - Asymptotic of mean value

KW - Elliptic curve over finite fields

KW - Shifted multiplicative function

UR - http://www.scopus.com/inward/record.url?scp=84934896159&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2015.04.015

DO - 10.1016/j.jnt.2015.04.015

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AN - SCOPUS:84934896159

SN - 0022-314X

VL - 157

SP - 37

EP - 53

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -