Abstract
We study a Ramanujan-Selberg continued fraction S(τ) by employing the modular function theory. We first find modular equations of S(τ) of level n for every positive integer n by using affine models of modular curves. This is an extension of Baruah-Saikia's results for level n=3, 5 and 7. We further show that the ray class field modulo 4 over an imaginary quadratic field K is obtained by the value of S2(τ), and we prove the integrality of 1/S(τ) to find its class polynomial for K with τ∈K∩H, where H is the complex upper half plane.
Original language | English |
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Pages (from-to) | 373-394 |
Number of pages | 22 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 438 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jun 2016 |
Bibliographical note
Publisher Copyright:© 2016 Elsevier Inc.
Keywords
- Class field theory
- Modular function
- Ramanujan continued fraction