Multiple Franel integrals

GRH Greaves; Richard Hall; M N Huxley; Julie C. Wilson

doi:10.1112/S0025579300013711

Multiple Franel integrals

GRH Greaves, Richard Hall, M N Huxley, Julie C. Wilson

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

Abstract

Let
p(x) = [x]-x + l/2 (1)
and Ax,A2,...,An, ax,a2,... ,an be positive integers. We consider the
related integrals
I(AX,A2, ...,An)=\ p(AlX)p(A2x).. .p(Anx)dx (2)
0
and
J{ax,a2,...,an) = | p[-)p[-)...p[ — )dx. (3)

Original language	English
Pages (from-to)	51-70
Number of pages	20
Journal	Mathematika
Volume	40
Issue number	1
DOIs	https://doi.org/10.1112/S0025579300013711
Publication status	Published - Jun 1993

Keywords

NUMBER THEORY;
Diophantine approximation;
Distribution modulo one

Access to Document

10.1112/S0025579300013711

Cite this

@article{f6648d0b066d4aa2aa4168cf4397471f,

title = "Multiple Franel integrals",

abstract = "Let p(x) = [x]-x + l/2 (1) and Ax,A2,...,An, ax,a2,... ,an be positive integers. We consider the related integrals I(AX,A2, ...,An)=\ p(AlX)p(A2x).. .p(Anx)dx (2) 0 and J{ax,a2,...,an) = | p[-)p[-)...p[ — )dx. (3)",

keywords = "NUMBER THEORY; , Diophantine approximation; , Distribution modulo one",

author = "GRH Greaves and Richard Hall and Huxley, {M N} and Wilson, {Julie C.}",

year = "1993",

month = jun,

doi = "10.1112/S0025579300013711",

language = "English",

volume = "40",

pages = "51--70",

journal = "Mathematika",

issn = "2041-7942",

publisher = "University College London",

number = "1",

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TY - JOUR

T1 - Multiple Franel integrals

AU - Greaves, GRH

AU - Hall, Richard

AU - Huxley, M N

AU - Wilson, Julie C.

PY - 1993/6

Y1 - 1993/6

N2 - Let p(x) = [x]-x + l/2 (1) and Ax,A2,...,An, ax,a2,... ,an be positive integers. We consider the related integrals I(AX,A2, ...,An)=\ p(AlX)p(A2x).. .p(Anx)dx (2) 0 and J{ax,a2,...,an) = | p[-)p[-)...p[ — )dx. (3)

AB - Let p(x) = [x]-x + l/2 (1) and Ax,A2,...,An, ax,a2,... ,an be positive integers. We consider the related integrals I(AX,A2, ...,An)=\ p(AlX)p(A2x).. .p(Anx)dx (2) 0 and J{ax,a2,...,an) = | p[-)p[-)...p[ — )dx. (3)

KW - NUMBER THEORY;

KW - Diophantine approximation;

KW - Distribution modulo one

U2 - 10.1112/S0025579300013711

DO - 10.1112/S0025579300013711

M3 - Article

SN - 2041-7942

VL - 40

SP - 51

EP - 70

JO - Mathematika

JF - Mathematika

IS - 1

ER -