On families of counting functions of number fields and hyperbolic manifolds of dimensions two and three
Artin formalism and heat kernels.
On Cramér's theorem for general Euler products with functional equation.
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Effective bounds for Faltings’s delta function
In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces , nowadays called Faltings’s delta function and here denoted by . For a given compact Riemann surface of genus , the invariant is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space of genus curves determined by to its boundary . In this paper we begin by revisiting a formula derived in [14],...
Unipotent vector bundles and higher-order non-holomorphic Eisenstein series
Higher-order non-holomorphic Eisenstein series associated to a Fuchsian group are defined by twisting the series expansion for classical non-holomorphic Eisenstein series by powers of modular symbols. Their functional identities include multiplicative and additive factors, making them distinct from classical Eisenstein series. In this article we prove the meromorphic continuation of these series and establish their functional equations which relate values at and . In addition, we construct...
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