Slim exceptional sets and the asymptotic formula in Waring’s problem

2003 ◽  
Vol 134 (2) ◽  
pp. 193-206 ◽  
Author(s):  
TREVOR D. WOOLEY
Keyword(s):  
Asymptotic Formula ◽  
Waring’S Problem ◽  
Exceptional Sets ◽  
Waring's Problem

scholarly journals A light-weight version of Waring's problem

2004 ◽  
Vol 76 (3) ◽  
pp. 303-316 ◽  
Author(s):  
Trevor D. Wooley
Keyword(s):  
Asymptotic Formula ◽  
Large Integer ◽  
Light Weight ◽  
Natural Numbers ◽  
Waring’S Problem ◽  
Waring's Problem ◽  
Large Solutions ◽  
Homogeneous Weight

AbstractAn asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.

Asymptotic formula in a generalized Waring's problem

1967 ◽  
Vol 63 (1) ◽  
pp. 87-98 ◽  
Author(s):  
K. Thanigasalam
Keyword(s):  
Asymptotic Formula ◽  
Waring’S Problem ◽  
Waring's Problem

Introduction. In the classical Waring's problem, the following asymptotic formula was established by Vinogradov (see Vinogradov (2), Chapter VII).

Note on the representation of integers as sums of certain powers

1969 ◽  
Vol 65 (2) ◽  
pp. 445-446 ◽  
Author(s):  
K. Thanigasalam
Keyword(s):  
Asymptotic Formula ◽  
Natural Number ◽  
Natural Numbers ◽  
Waring’S Problem ◽  
Waring's Problem ◽  
Representation Of Integers ◽  
Image Position ◽  
Large Natural Number

In the paper entitled ‘Asymptotic formula in a generalized Waring's problem’, I established an asymptotic formula for the number of representations of a large natural number N in the formwhere x1, x2, …, x7 and k are natural numbers with k ≥ 4 (see (2) Theorem 2).

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