Video library: I. S. Rezvyakova, Zeros of linear combinations of Hecke $L$-functions on the critical line

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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
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. Language: English