| Abstrakt: |
We study the distribution of the zeros of functions of the form f( s) = h( s) ± h(2 a − s), where h( s) is a meromorphic function, real on the real line, a is a real number. One of our results establishes sufficient conditions under which all but finitely many of the zeros of f( s) lie on the line ℜ s = a, called the critical line for the function f( s), and that they are simple, provided that all but finitely many of the zeros of h( s) lie on the half-plane ℜ s < a. This result can be regarded as a generalization of the necessary condition of stability for the function h( s), in the Hermite-Biehler theorem. We apply our results to the study of translations of the Riemann Zeta Function and L functions, and integrals of Eisenstein Series, among others. [ABSTRACT FROM AUTHOR] |
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