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A larger GL 2 large sieve in the level aspect

100%
Djanković G.
Open Mathematics
|
2012
|
tom 10
|
nr 2
748-760
EN
In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.
2
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Completely normal elements in some finite abelian extensions

100%
Koo J., Shin D.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1725-1731
EN
We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.
3
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Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields

84%
Kim C., Koo J.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1389-1402
EN
We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.
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