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Some Results on Definite Quadratic Forms
Author(s) -
Erdös Paul,
Ko Chao
Publication year - 1938
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s1-13.3.217
Subject(s) - citation , quadratic equation , computer science , combinatorics , library science , information retrieval , mathematics , mathematical economics , geometry
f(z) is decomposable. It is an interesting problem to find non-decomposable forms for which D is large. Let pn be the largest value of D for a non-decomposabIe form in n variables. MordeIl$ has proved that there exist non-decomposable forms for n = 6, 7, and 8. We5 have proved that there exist non-decomposable forms for every n > 8, and that, for n > 189, /LfL > (n17e>/13. In $2, we prove that for certuim sequences of n, there exist nondecomposable forms with D > (1. l)n. It is not difficult to show that pn > ( 1 I l)?‘, for all sufficiently large m, but we do not give the proof here, since it is rather complicated. --. ~ -