The Representation of Numbers By Sums of Fourth Powers

Hunter, W.N.

doi:10.1112/jlms/s1-16.3.177

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There Exist a And B Such That1

Introduction1

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1965

2012

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Cited by 7 publications

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“…Thus I showed [14] that 8 < v(4) < 12. Davenport improved this to v(4) < 11 and Hunter [6] improved it further to 9<v(4)<10.…”

Section: There Exist a And B Such Thatmentioning

confidence: 97%

Equal Sums of Like Powers

Wright

1965

Can. math. bull.

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“…Thus I showed [14] that 8 < v(4) < 12. Davenport improved this to v(4) < 11 and Hunter [6] improved it further to 9<v(4)<10.…”

Section: There Exist a And B Such Thatmentioning

confidence: 97%

Equal Sums of Like Powers

Wright

1965

Can. math. bull.

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“…It seems likely that four cubes suffice for all integers. A similar situation prevails for decompositions into fourth powers (Hunter, 1941): ten fourth powers always suffice and there are numbers which cannot be decomposed into eight (signed) fourth powers, hence »(4) is either 9 or 10.…”

Section: Introductionmentioning

confidence: 99%

Major arcs in the four cubes problem

Szekeres

1978

J. Aust. Math. Soc.

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There is an old conjecture that every integer can be decomposed into four (positive or negative) perfect cubes. More specifically one would like to know the asymptotic number of solutions of when a large bound N is placed on the parts TW, -. Using the circle method it is shown that the number of such representations of n when N -> oo is asymptotically equal to C(«). N for a certain positive constant C(n), provided that the contribution of the minor arcs can be neglected.The dependence of C(«) on n is exhibited explicitly by expressing C(«) as an infinite product. The formula is of heuristic value only since the minor arcs cannot be handled at present.

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The Thirties

Narkiewicz

2012

Springer Monographs in Mathematics

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The Representation of Numbers By Sums of Fourth Powers

Cited by 7 publications

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Equal Sums of Like Powers

Equal Sums of Like Powers

Major arcs in the four cubes problem

The Thirties

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