Affiliation:
1. Department of Mathematics , University of Prishtina , Mother Theresa, no. 5 , Prishtina , Kosovo
Abstract
Abstract
In this paper, we prove some conditional results about the order of zero at central point s = 1/2 of the Rankin-Selberg L-function L(s, πf
× π͠′
f
). Then, we give an upper bound for the height of the first zero with positive imaginary part of L(s, πf
× π͠′
f
). We apply our results to automorphic L-functions.
Reference15 articles.
1. Avdispahić, M.—Smajlović, A: Explicit formula for a fundamental class of functions, Bull. Belg. Math. Soc. Simon Stevin 12 (2005), 569–587.
2. Cogdell, J.W.: L-functions and converse theorems for GLn, Park City Lect. Notes, available at http://www.math.ohio-state.edu/~cogdell.
3. Gelbart, S.—Shahidi, F.: Boundedness of automorphic L-functions in vertical strips, J. Am. Math. Soc. 14, (2001), 79–107.
4. Jacquet, H.—Shalika, J. A.: On Euler products and the classification of automorphic representations, I. Am. J. Math. 103 (1981), 499–558.
5. Jacquet, H.—Shalika, J. A.: On Euler products and the classification of automorphic representations II, Am. J. Math. 103 (1981), 777–815.