Bulletin of the Belgian Mathematical Society - Simon Stevin

Explicit formula for a fundamental class of functions

Muharem Avdispahić and Lejla Smajlović

Full-text: Open access


The purpose of this paper is to prove an analogue of A. Weil's explicit formula for a fundamental class of functions, i.e. the class of meromorphic functions that have an Euler sum representation and satisfy certain a functional equation. The advance of this explicit formula is that it enlarges the class of allowed test functions, from the class of functions with bounded Jordan variation to the class of functions of $\phi $-bounded variation. A condition posed to the test function at zero is also reconsidered.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 4 (2005), 569-587.

First available in Project Euclid: 5 December 2005

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 26A45: Functions of bounded variation, generalizations

Explicit formula $\phi $ - variation Weil's functional


Avdispahić, Muharem; Smajlović, Lejla. Explicit formula for a fundamental class of functions. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 4, 569--587. doi:10.36045/bbms/1133793345. https://projecteuclid.org/euclid.bbms/1133793345

Export citation