Six Exponentials Theorem
المؤلف:
Finch, S. R.
المصدر:
"Powers of 3/2 Modulo One." §2.30.1 in Mathematical Constants. Cambridge, England: Cambridge University Press
الجزء والصفحة:
...
2-2-2021
2398
Six Exponentials Theorem
Let 
and 
be two sets of complex numbers linearly independent over the rationals. Then at least one of
is transcendental (Waldschmidt 1979, p. 3.5). This theorem is due to Siegel, Schneider, Lang, and Ramachandra. The corresponding statement obtained by replacing 
with 
is called the four exponentials conjecture and remains unproven.
REFERENCES:
Finch, S. R. "Powers of 3/2 Modulo One." §2.30.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 194-199, 2003.
Ramachandra, K. "Contributions to the Theory of Transcendental Numbers. I, II." Acta Arith. 14, 65-78, 1967-68.
Ramachandra, K. and Srinivasan, S. "A Note to a Paper: 'Contributions to the Theory of Transcendental Numbers. I, II' by Ramachandra on Transcendental Numbers." Hardy-Ramanujan J. 6, 37-44, 1983.
Waldschmidt, M. Transcendence Methods. Queen's Papers in Pure and Applied Mathematics, No. 52. Kingston, Ontario, Canada: Queen's University, 1979.
Waldschmidt, M. "On the Transcendence Method of Gel'fond and Schneider in Several Variables." In New Advances in Transcendence Theory (Ed. A. Baker). Cambridge, England: Cambridge University Press, pp. 375-398, 1988.
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
