Timeline for A conjecture about algebraic values of $(-q;\,-q)_\infty/(q;\,q)_\infty$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2016 at 4:58 | comment | added | Vladimir Reshetnikov | I found an interesting paper on this topic: Ramanujan’s Class Invariants With Applications to the Values of q–Continued Fractions and Theta Functions | |
| Nov 23, 2016 at 19:54 | comment | added | Noam D. Elkies | You're welcome. But asking to "determine which exactly algebraic number corresponds to a given point" is probably askign too much. Knowing the conjugates will make it easier to calculate the minimal polynomial, but -- as with the "Kronecker Jugendtraum" -- I don't think you can expect a recipe for a general answer that you could specialize to formulas like $f(3/5) = \sqrt[8]{2} \cdot \sqrt[4]{9 \sqrt{5}+5 \sqrt{15}-11 \sqrt{3}-19}$; even the degree of the algebraic number will involve the class number of an imaginary quadratic field. | |
| Nov 23, 2016 at 17:15 | comment | added | Vladimir Reshetnikov | Thanks! Could you recommend a book that would explain how to determine which exactly algebraic number corresponds to a given point? | |
| Nov 23, 2016 at 17:14 | vote | accept | Vladimir Reshetnikov | ||
| Nov 23, 2016 at 16:50 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
explain "CM" and add a final sentence about the existence of further applications of CM theory to such numbers.
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| Nov 23, 2016 at 16:48 | comment | added | Noam D. Elkies | Yes, sorry -- I only realized later that I should have expanded the acronym "CM" when I first introduced it. I'll do so next. | |
| Nov 23, 2016 at 9:24 | comment | added | Fedor Petrov | @T.Amdeberhan complex multiplication | |
| Nov 23, 2016 at 5:19 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
Inserted the missing factors of $(\pm q)^{-1/24}$
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| Nov 23, 2016 at 5:06 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |