A multidimensional version of a result of Davenport-Erdos

O. Yeat Chan; Geumlan Choi; Alexandra Zaharescu

A multidimensional version of a result of Davenport-Erdos

O. Yeat Chan, Geumlan Choi, Alexandra Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Davenport and Erdos showed that the distribution of values of sums of the form S_h(x) = ∑_m=x+1^x+h (m/p), where p is a prime and (m/p) is the Legendre symbol, is normal as h,p → ∞ such that log h/log p → 0. We prove a similar result for sums of the form S _h(x₁,..., x_n) = ∑_z1=x1+1 ^x1+h ⋯ ∑_zn=xn+1^xn+h (z₁ +...+z_n/p).

Original language	English (US)
Journal	Journal of Integer Sequences
Volume	6
Issue number	2
State	Published - 2003

Keywords

Legendre symbol
Normal distribution

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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title = "A multidimensional version of a result of Davenport-Erdos",

abstract = "Davenport and Erdos showed that the distribution of values of sums of the form Sh(x) = ∑m=x+1x+h (m/p), where p is a prime and (m/p) is the Legendre symbol, is normal as h,p → ∞ such that log h/log p → 0. We prove a similar result for sums of the form S h(x1,..., xn) = ∑z1=x1+1 x1+h ⋯ ∑zn=xn+1xn+h (z1 +...+zn/p).",

keywords = "Legendre symbol, Normal distribution",

author = "Chan, {O. Yeat} and Geumlan Choi and Alexandra Zaharescu",

year = "2003",

language = "English (US)",

volume = "6",

journal = "Journal of Integer Sequences",

issn = "1530-7638",

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AU - Chan, O. Yeat

AU - Choi, Geumlan

AU - Zaharescu, Alexandra

PY - 2003

Y1 - 2003

N2 - Davenport and Erdos showed that the distribution of values of sums of the form Sh(x) = ∑m=x+1x+h (m/p), where p is a prime and (m/p) is the Legendre symbol, is normal as h,p → ∞ such that log h/log p → 0. We prove a similar result for sums of the form S h(x1,..., xn) = ∑z1=x1+1 x1+h ⋯ ∑zn=xn+1xn+h (z1 +...+zn/p).

AB - Davenport and Erdos showed that the distribution of values of sums of the form Sh(x) = ∑m=x+1x+h (m/p), where p is a prime and (m/p) is the Legendre symbol, is normal as h,p → ∞ such that log h/log p → 0. We prove a similar result for sums of the form S h(x1,..., xn) = ∑z1=x1+1 x1+h ⋯ ∑zn=xn+1xn+h (z1 +...+zn/p).

KW - Legendre symbol

KW - Normal distribution

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JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 2

ER -

A multidimensional version of a result of Davenport-Erdos

Abstract

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