On the superior bound of the number of representations of an integer by binary forms of the fourth degree. (Q2594065)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the superior bound of the number of representations of an integer by binary forms of the fourth degree. |
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On the superior bound of the number of representations of an integer by binary forms of the fourth degree. (English)
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1939
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Nach einer von \textit{C. L. Siegel} (Abh. Preuß. Akad. Wiss. Phys.-math. Kl. 1929, Nr. 1; F.~d.~M. 56\(_{\text{I}}\), 180-184) stammenden Methode beweist Verf., daß die diophantische Gleichung \[ a_0x^4+a_1x^3y+a_2x^2y^2+a_3xy^3+a_4y^4=1 \] höchstens 20 Lösungen besitzt, wenn \[ J \equiv 2a_2^3-9a_1a_2a_3+27a_1^2a_4-72a_0a_2a_4+27a_0a_3^2=0 \] ist.
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