We prove that H-invariants and the conductor of the function F belonging to the Selberg class can be represented as special values of (a meromorphic continuation of) a ”superzeta” function arising from non-trivial zeros of F .

In order to determine the habitat preferred by Myodes (before Clethrionomys) glareolus and the corresponding Puumala hantavirus seroprevalence in those habitats, we captured rodents simultaneously in three significantly different habitats. We compared trapping success and presence of virus per habitat during an ongoing epidemic in order to test the hypothesis of a density-dependent seroprevalence. Our study showed that bank vole population density, as well as Puumala virus seroprevalence, were habitat dependent. Apodemus sylvaticus was found more vulnerable for deteriorating habitat conditions than M. glareolus and could play a role as vehicle for Puumala virus and as mediator for inter- and conspecific virus transmission.

Using an integral representation of the logarithmic derivative of the corresponding Selberg zeta function, we prove Stieltjes-type expressions for higher Euler constants on non-compact hyperbolic Riemann surfaces of finite volume with cusps. New upper and lower bounds are given for the constant term of this logarithmic derivative in a case of interest in Arakelov geometry.

Explicit formula for the fundamental class of functions ( Z, Z,Φ ) , introduced by J. Jorgenson and S. Lang, is given a new form valid for a more general fudge factor Φ. This is done for a larger class of test functions of generalized bounded variation.

Taking Weil’s point on adelic nature of explicit formulas, we extend the class of test functions to which his formula in Barner‐Burnol version holds.