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A REMARK OF EISENSTEIN SERIES AND THETA SERIES
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 Title & Authors
A REMARK OF EISENSTEIN SERIES AND THETA SERIES
Kim, Dae-Yeoul; Koo, Ja-Kyung;
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 Abstract
As a by-product of [5], we produce algebraic integers of certain values of quotients of Eisenstein series. And we consider the relation of and . That is,we show that $\Theta_3(0,\tau^n)=\Theta_3(0,\tau),\bigtriangleup(0,\tau)=\bigtriangleup(0,\tau^n)$ and for some .
 Keywords
infinite product;Eisenstein series;theta serise;
 Language
English
 Cited by
1.
Some refined higher type adjunction inequalities on 4-manifolds, International Journal of Mathematics, 2015, 26, 05, 1550038  crossref(new windwow)
 References
1.
R. J. Baxter, A directed proof of Kim's identities, J. Phys. A: Math. Gen. 31 (1998), 1105-1108. crossref(new window)

2.
B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's remarkable product of theta-functions, Proc. Edinburgh Math. Soc. 40 (1997), 583-612. crossref(new window)

3.
K. Chandrasekharan, Elliptic Functions, Springer-Verlag, Grundlehren der mathematischen wissenschaften 281, 1985.

4.
D. Kim and J. K. Koo, Algebraic integer as values of elliptic functions, Acta Arith. 100 (2001), 105-116. crossref(new window)

5.
D. Kim and J. K. Koo, Algebraic integers as values of Eisenstein series, Submitted.

6.
D. Kim and J. K. Koo, Integrability as values of cusp forms in imaginary quadratic, Comm. Korean Math. Soc. 16 (2001), 585-594.

7.
D. Kim and J. K. Koo, Trnascendental numbers as values of elliptic functions, Bull. Korean Math. Soc. 37 (2000), 675-683.

8.
D. Kim and J. K. Koo, As values of transcendental and algebraic numbers of infinite products in imaginary quadratics(Korean), Submitted.

9.
D. Kim, Asymmetric XXZ chain at the andtiferromagnetic transition: spectra and partition functions, J. Phys. A: Math. Gen. 30 (1997), 3817-3836. crossref(new window)

10.
S. Lang, Elliptic Functions, Addison-Wesley, 1973.

11.
J. -P. Serre, A course in Arithmetic, Springer-Verlag, 1973.

12.
J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer - Verlag, New York, 1994.