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International Chinese-Russian conference on Number Theory
October 9, 2012 12:30, Moscow, Steklov Mathematical Institute

Zeros of linear combinations of Hecke $L$-functions on the critical line

I. S. Rezvyakova
 Video records: Flash Video 260.5 Mb Flash Video 1,558.2 Mb MP4 260.5 Mb

Abstract: Let us consider a linear combination of Hecke $L$-functions associated with the characters of the ideal class group of the imaginary quadratic field $\mathbb{Q}(\sqrt{-D})$. In general, such linear combinations have many non-trivial zeros outside the critical line. Nevertheless, under certain natural conditions we shall show that the critical line is an exceptional set, which contains a large proportion of their non-trivial zeros.