Difference of modular functions and their CM value factorization
نویسندگان
چکیده
منابع مشابه
Traces of Cm Values of Modular Functions
Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also st...
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The purpose of this note is to report on recent joint work with J. Funke, P. Jenkins, and K. Ono on the traces of CM values of modular functions and some applications [BF], [BJO].
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(1) zd = { i √ d 2 if d ≡ 0 (mod 4), −1+i √ d 2 if d ≡ 3 (mod 4). The j-function has the remarkable property that j(zd) is an algebraic integer of degree h(−d), the class number of K = Q(zd). In fact, K(j(zd)) is the Hilbert class field of K [4]. The first few values of j(zd) are: j(z3) = 0, j(z4) = 12 , j(z7) = −153, j(z8) = 20, j(z11) = −323 j(z15) = −191025−85995√5 2 , j(z19) = −963, j(z20) ...
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چکیده ندارد.
15 صفحه اولDifference balanced functions and their generalized difference sets
Difference balanced functions from F∗ q to Fq are closely related to combinatorial designs and naturally define p-ary sequences with the ideal two-level autocorrelation. In the literature, all existing such functions are associated with the d-homogeneous property, and it was conjectured by Gong and Song that difference balanced functions must be d-homogeneous. First we characterize difference b...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2018
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7479