The Chowla-Selberg formula
نویسندگان
چکیده
منابع مشابه
Chowla-selberg Formula and Colmez’s Conjecture
In this paper, we reinterpret the Colmez conjecture on Faltings’ height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving Faltings’ height of a CM abelian surface and arithmetic intersection numbers, and prove that Colmez’s conjecture for CM abelian surfaces is equivalent to the cuspitality of this modular form.
متن کاملThe Chowla–Selberg Formula and The Colmez Conjecture
In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.
متن کاملMultidimensional extension of the generalized Chowla–Selberg formula
After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form ζA,~b,q(s) = ∑ ~n∈Z (~nA~n+~b~n+ q)−s, with A the p× p matrix of a quadratic form, ~b a p vector and q...
متن کاملThe Chowla-Selberg Formula for Quartic Abelian CM Fields
We provide explicit analogues of the Chowla-Selberg formula for quartic abelian CM fields. This consists of two main parts. First, we implement an algorithm to compute the CM points at which we will evaluate a certain Hilbert modular function. Second, we exhibit families of quartic fields for which we can determine the precise form of the analogue of the product of gamma values.
متن کاملAn Analogue of the Chowla–selberg Formula for Several Automorphic L-functions
In this paper, we will give a certain formula for the Riemann zeta function that expresses the Riemann zeta function by an infinte series consisting of KBessel functions. Such an infinite series expression can be regarded as an analogue of the Chowla-Selberg formula. Roughly speaking, the Chowla-Selberg formula is the formula that expresses the Epstein zeta-function by an infinite series consis...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1983
ISSN: 0022-314X
DOI: 10.1016/0022-314x(83)90022-7