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On the gaps between values of binary quadratic forms

  • Jörg Brüdern (a1) (a2) and Rainer Dietmann (a1) (a3)

Abstract

Among the values of a binary quadratic form, there are many twins of fixed distance. This is shown in quantitative form. For quadratic forms of discriminant −4 or 8 a corresponding result is obtained for triplets.

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1.Bernays, P., Über die Darstellung von positiven, ganzen Zahlen durch die primitiven binären quadratischen Formen einer nichtquadratischen Diskriminante, Dissertation, Universität Göttingen (1912).
2.Dickson, L. E., Studies in the theory of numbers (Chicago University Press, 1930).
3.Dietmann, R., Small solutions of quadratic Diophantine equations, Proc. Lond. Math. Soc. 86 (2003), 545582.
4.Gauss, C. F., Disquisitiones arithmeticae (Leipzig, 1801).
5.Goldston, D. A., Graham, S. W., Pintz, J. and Yildirim, C. Y., Small gaps between products of two primes, Proc. Lond. Math. Soc. (3) 98 (2009), 741774.
6.Goldston, D. A., Pintz, J. and Yildirim, C. Y., Primes in tuples, I, Annals Math. (2) 170 (2009), 819862.
7.Hablizel, M., Beschränkte Lücken zwischen Werten von Normformen, Dissertation, Universität Stuttgart (2008).
8.Hooley, C., On the intervals between numbers that are sums of two squares, II, J. Number Theory 5 (1973), 215217.
9.Lefton, P., On the Galois groups of cubics and trinomials, Acta Arith. 35 (1979), 239246.
10.Thorne, F., Bounded gaps between products of primes with applications to ideal class groups and elliptic curves, Int. Math. Res. Not. 2008(5) (2008), rnm156.

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On the gaps between values of binary quadratic forms

  • Jörg Brüdern (a1) (a2) and Rainer Dietmann (a1) (a3)

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