Multiplicative Dedekind \eta -function and representations of finite groups
نویسندگان
چکیده
منابع مشابه
Multiplicative Dedekind η-function and representations of finite groups
In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative η−products). This problem is open. We find metacyclic groups with such property and describe the Sylow p-subgroups, p 6= 2, for such groups. We als...
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We extend the methods of Van der Poorten and Chapman [7] for explicitly evaluating the Dedekind eta function at quadratic irrationalities. Via Hecke L-series we obtain evaluations in some new cases. Specifically we provide further evaluations at points in imaginary quadratic number fields with class numbers up to four. We also describe techniques, which make use of modular equations, which prov...
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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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Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b − 4ac = d, a > 0, gcd(a, b, c) = 1. The value of |η ( (b + √ d)/2a ) | is determined explicitly, where η(z) is Dedekind’s eta function η(z) = e ∞ ∏ m=1 (1− e) ( im(z) > 0 ) .
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A micro-introduction to the theory of representations of finite groups.
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2005
ISSN: 1246-7405
DOI: 10.5802/jtnb.495