Multiplicative $\eta $-quotients
نویسندگان
چکیده
منابع مشابه
Eta-quotients and Elliptic Curves
In this paper we list all the weight 2 newforms f(τ) that are products and quotients of the Dedekind eta-function η(τ) := q ∞ Y n=1 (1− q), where q := e2πiτ . There are twelve such f(τ), and we give a model for the strong Weil curve E whose Hasse-Weil L−function is the Mellin transform for each of them. Five of the f(τ) have complex multiplication, and we give elementary formulae for their Four...
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In this paper we present an algorithm which can prove algebraic relations involving η-quotients, where η is the Dedekind eta function. 1. The Problem Let N be a positive integer throughout this paper. We denote by R(N) the set of integer sequences r = (rδ)δ|N indexed by the positive divisors δ of N ; r̃ = (r̃δ)δ|N is defined by r̃δ := rN/δ. For r ∈ R(N) we define an associated η-quotient as f(r)(τ...
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We determine the conditions under which singular values of multiple η-quotients of square-free level, not necessarily prime to 6, yield class invariants, that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index 2 ′ −1 when k > 2 primes dividing the level are ramified in the imaginary...
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Inspired by Riemann’s work on certain quotients of the Dedekind Eta function, in this paper we investigate the value distribution of quotients of values of the Dedekind Eta function in the complex plane, using the form η(Ajz) η(Aj−1z) , where Aj−1 and Aj are matrices whose rows are the coordinates of consecutive visible lattice points in a dilation XΩ of a fixed region Ω in R, and z is a fixed ...
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We examine a class of modular functions for Γ(N) whose values generate ring class fields of imaginary quadratic orders. This fact leads to a new algorithm for constructing elliptic curves with complex multiplication. The difficulties arising when the genus of X0(N) is not zero are overcome by computing certain modular polynomials. Being a product of four η-functions, the proposed modular functi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1996
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-96-01743-6