KRONECKER LIMIT FUNCTIONS AND AN EXTENSION OF THE ROHRLICH–JENSEN FORMULA
نویسندگان
چکیده
Abstract In [20], Rohrlich proved a modular analog of Jensen’s formula. Under certain conditions, the Rohrlich–Jensen formula expresses an integral log-norm $\log \Vert f $ ${\mathrm {PSL}}(2,{\mathbb {Z}})$ form in terms Dedekind Delta function evaluated at divisor . [2], authors re-interpreted as evaluating regularized inner product and extended result to compute with what amounts powers Hauptmodul $\mathrm {PSL}(2,{\mathbb present article, we revisit prove that case any Fuchsian group first kind one cusp it can be viewed special values two Poincaré series, which is Niebur–Poincaré series other resolvent kernel Laplacian. The seen type Maass–Selberg relation. this form, develop associated $\Gamma by employing Kronecker limit kernel. We examples our main result: First, when full , thus reproving theorems from [2]; second Atkin–Lehner _{0}(N)^+$ where explicit computations products are given for levels N quotient space $\overline {\Gamma _{0}(N)^+}\backslash \mathbb {H}$ has genus zero, one, two.
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15 صفحه اولNonholomorphic Eisenstein series, the Kronecker limit formula, and the hyperbolic Laplacian
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2023
ISSN: ['0027-7630', '2152-6842']
DOI: https://doi.org/10.1017/nmj.2023.7