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Class Numbers and Short Sums of Kronecker Symbols

✍ Scribed by A. Schinzel; J. Urbanowicz; P. Van Wamelen

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
313 KB
Volume
78
Category
Article
ISSN
0022-314X

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✦ Synopsis

The sets P = are of interest for the following reason. For each ==0, 1 and (q 1 , q 2 ) # P = the set of all D # F prime to r satisfying card C(D, q 1 , q 2 )== is, by virtue of (1.7), the intersection of F with the union of some arithmetic progressions with the first term D 0 and the difference r((r 3 , 8)Γ‚(r, 8)) sgn D 0 . Hence the condition card C(D, q 1 , q 2 )== if fulfilled by one D # F prime to r is fulfilled by infinitely many such D. The condition (1.10) is justified by the formulae (1.4), (1.5), and (1.6); it permits us to retain in the theorem only essentially different cases.

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