Automorphic forms of nonnegative dimension and exponential sums.
نویسندگان
چکیده
منابع مشابه
The Dimension of Spaces of Automorphic Forms
1. The trace formula of Selberg reduces the problem of calculating the dimension of a space of automorphic forms, at least when there is a compact fundamental domain, to the evaluation of certain integrals. Some of these integrals have been evaluated by Selberg. An apparently different class of definite integrals has occurred in Harish-Chandra’s investigations of the representations of semi-sim...
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I will first formulate a problem in the theory of group representations and show how to solve it; then I will discuss the relation of this problem to the theory of automorphic forms. Since there is no point in striving for maximum generality, I start with a connected semisimple group G with finite center. An irreducible unitary representaiton π of G on the Hilbert space H is said to be square-i...
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More general results, including arbitrary Fuchsian groups, can be found in the paper [Bo2] of Borcherds, Sect. 7. Most of them have been proved by the Selberg trace formula, see [Iv] and also [Fi]. The Selberg trace formula in its standard form causes the restriction that the weight is > 2. Borcherds mentions that “with a bit more care this also works for weight 2”. As we mentioned, this bit mo...
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We develop some of the theory of automorphic forms in the function field setting. As an application, we find formulas for the number of ways a polynomial over a finite field can be written as a sum of k squares, k ≥ 2. Given a finite field Fq with q odd, we want to determine how many ways a polynomial in Fq[T ] can be written as a sum of k squares. For k ≥ 3 (or k = 2, −1 not a square in Fq), t...
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There are infinitely many hyperbolic transforms of complex abelian surfaces. The corresponding universal covers change from the complex plane to the unit ball, from flat to hyperbolic metrics. Looking back to Jacobi’s periodic functions we were able to construct 2-dimensional abelian functions transformable to automorphic forms on the ball. In this article we prove explicit dimension formulas f...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1960
ISSN: 0026-2285
DOI: 10.1307/mmj/1028998437