논문KCI 등재
On the infinite products derived from theta series II
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Let k be an imaginary quadratic field, ㆍ the complex upper half plane, and let τ ∈ㆍ ∩ k, q = eπiτ . For n, t ∈ Z+ with 1 ≤ t ≤ n − 1, set n = ㆍ·2l (ㆍ = 2, 3, 5, 7, 9, 13, 15) with l ≥ 0 integer. Then we show that [수식](1 − qnm−t)(1 − qnm−(n−t)) are algebraic numbers
Abstract
Let k be an imaginary quadratic field, ㆍ the complex upper half plane, and let τ ∈ㆍ ∩ k, q = eπiτ . For n, t ∈ Z+ with 1 ≤ t ≤ n − 1, set n = ㆍ·2l (ㆍ = 2, 3, 5, 7, 9, 13, 15) with l ≥ 0 integer. Then we show that [수식](1 − qnm−t)(1 − qnm−(n−t)) are algebraic numbers
참고문헌 (10)
- B. C. Berndt, "Ramanujan’s Notebooks. Part II" (1989), Springer-Verlag
- B. C. Berndt, "Ramanujan’s Notebooks. Part III" (1991), Springer-Verlag
- B. C. Berndt, "Ramanujan’s Notebooks. Part IV" (1994), Springer-Verlag
- D. Kim, "Algebraic integers as values of elliptic functions", Acta Arithmetica, 100(2), pp.105~116 (2001)
- 김대열, "On the infinite products derived from theta series I", 대한수학회보, 44(1), pp.55~107 (2007), 대한수학회
- S. Lang, "Elliptic Functions" (1973), Addison-Wesley Publishing Co., Inc.
- C. L. Siegel, "Transcendental Numbers, Annals of Mathematics Studies, no. 16" (1949), Princeton University Press
- A. V. Sills, "On identities of the Rogers-Ramanujan type", Ramanujan Journal, 11(3), pp.403~429 (2006)
- M. Waldschmidt, "Nombres Transcendants, Lecture Notes in Mathematics, Vol. 402" (1974), Springer-Verlag
- E. T. Whittaker, "A Course of Modern Analysis, An introduction to the general theory of infinite processes and of analytic functions: with an account of the principal transcendental functions" (1962), Reprinted Cambridge University Press
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