## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Explicit formula for a fundamental class of functions

#### Abstract

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

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

Dates
First available in Project Euclid: 5 December 2005

https://projecteuclid.org/euclid.bbms/1133793345

Digital Object Identifier
doi:10.36045/bbms/1133793345

Mathematical Reviews number (MathSciNet)
MR2206001

Zentralblatt MATH identifier
1210.11097

#### Citation

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