The history of the problem is obscure, but W. W. Rouse Ball indicated (without citation) that it was first discussed by an "H. Davenport", possibly Harold Davenport.
Auxiliary types of sums occur in the theory, for example character sums; going back to Harold Davenport's thesis.
Harold Pinter | Davenport, Iowa | Harold Wilson | Harold Macmillan | Harold Bloom | Harold Godwinson | Davenport | Harold Lloyd | Harold Stassen | Harold Prince | J. Harold Ellens | Harold Holt | Sir Harold Hillier Gardens | Harold Washington | Harold Hitz Burton | Harold Alexander, 1st Earl Alexander of Tunis | Harold Peto | Harold & Kumar Go to White Castle | Harold Arlen | Harold | Lindsay Davenport | Harold Budd | Harold Eugene Edgerton | Harold Bauer | Jack Davenport | Harold von Schmidt | Harold Robbins | Harold Laski | Harold Gould | Harold Gillies |
More influenced by Harold Davenport, he proved Birch's theorem, one of the definitive results to come out of the Hardy–Littlewood circle method; it shows that odd-degree rational forms in a large enough set of variables must have zeroes.