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EXPLICIT FORMULAS FOR THE MODULAR EQUATION
"... Abstract. We determine a linear time algorithm for calculating the modular equation ΦN (X, J) for N = p1p2, where p1 and p2 are distinct primes. We provide N = 10 as an example. 1. ..."
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Abstract. We determine a linear time algorithm for calculating the modular equation ΦN (X, J) for N = p1p2, where p1 and p2 are distinct primes. We provide N = 10 as an example. 1.
Explicit formulas for the Hilbert symbol
 GEOMETRY & TOPOLOGY MONOGRAPHS VOLUME 3: INVITATION TO HIGHER LOCAL FIELDS PART I, SECTION 8, PAGES 81–89
, 2000
"... Recall that the Hilbert symbol for a local field K with finite residue field which contains a primitive pn th root of unity ζpn is a pairing ( ,)p n:K ∗ /K ∗pn × K ∗ ∗ pn /K → 〈ζpn〉, (α,β)p n = γΨK(α)−1 p, γ n = β, where ΨK:K ∗ → Gal(K ab /K) is the reciprocity map. ..."
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Recall that the Hilbert symbol for a local field K with finite residue field which contains a primitive pn th root of unity ζpn is a pairing ( ,)p n:K ∗ /K ∗pn × K ∗ ∗ pn /K → 〈ζpn〉, (α,β)p n = γΨK(α)−1 p, γ n = β, where ΨK:K ∗ → Gal(K ab /K) is the reciprocity map.
Exponential maps and explicit formulas
 GEOMETRY & TOPOLOGY MONOGRAPHS VOLUME 3: INVITATION TO HIGHER LOCAL FIELDS PART I, SECTION 9, PAGES 91–94
, 2000
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An explicit formula for the cubic Szegő equation
, 2013
"... We derive an explicit formula for the general solution of the cubic Szegő equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are quasiperiodic. ..."
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We derive an explicit formula for the general solution of the cubic Szegő equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are quasiperiodic.
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