On a unit group generated by special values of Siegel modular functions
نویسندگان
چکیده
منابع مشابه
On a unit group generated by special values of Siegel modular functions
There has been important progress in constructing units and Sunits associated to curves of genus 2 or 3. These approaches are based mainly on the consideration of properties of Jacobian varieties associated to hyperelliptic curves of genus 2 or 3. In this paper, we construct a unit group of the ray class field k6 of Q(exp(2πi/5)) modulo 6 with full rank by special values of Siegel modular funct...
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We consider certain abelian extensions K, k1 of Q(e2πi/5) and show by a method of Shimura that a normal basis of K over k1 can be given by special values of Siegel modular functions.
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Recently, Fukuda and Komatsu constructed units of a certain abelian extension of Q(exp(2π √ −1/5)) using special values of Siegel modular functions. In this paper, we determine the minimal polynomials of these units.
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and Hg is open in Zg(C); τ = (τjl) a generic point on Hg, so that k(2πiτ ) can be viewed as the field of rational functions on Zg/k; Γ = a congruence subgroup of Sp2g(Z) (equivalently, a subgroup of finite index if g > 1). We recall that the symplectic group Sp2g has dimension dimSp2g = 2g 2 + g; Rw(Γ, k) = k-vector-space of k-rational modular forms of weight w (a non-negative integer) relative...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1999
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-99-01118-7