{
  "id": "1408.3394",
  "version": "v3",
  "published": "2014-08-14T19:20:10.000Z",
  "updated": "2014-09-03T19:53:03.000Z",
  "title": "Mean-Value of Product of Shifted Multiplicative Functions and Average Number of Points on Elliptic Curves",
  "authors": [
    "R. Balasubramanian",
    "Sumit Giri"
  ],
  "comment": "In this version the overall presentation has been changed by keeping the main result fixed",
  "categories": [
    "math.NT"
  ],
  "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 $K(N)$, where $K(N)/\\log N$ is the expected number of primes such that a random elliptic curve over rationals has $N$ points when reduced over those primes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-15T05:26:50.000Z",
      "title": "Average Value of Product of Two Shifted Multiplicative Functions",
      "abstract": "If F and G are two 'good' multiplicative functions then we compute the average value of F(n-h)G(n) for any fixed integer h. We use this result to prove similar averaging when F and G differ from being multiplicative. We also compute average value of the constant K(N), which is related to certain prime counting function for elliptic curve over finite fields.",
      "comment": "This paper has been withdrawn due to some grammatical and writing errors. Also few more lines need to be added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-03T19:53:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "average value",
      "shifted multiplicative functions",
      "prime counting function",
      "elliptic curve",
      "finite fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.3394B"
    }
  }
}