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On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach

Irina Rezvyakova

Abstract

This is an article, published in Izvestiya: Mathematics, 2016, Volume 80, Issue 3, which complements arxiv:2411.18492

On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach

Abstract

This is an article, published in Izvestiya: Mathematics, 2016, Volume 80, Issue 3, which complements arxiv:2411.18492
Paper Structure (1 section, 3 theorems, 113 equations)

This paper contains 1 section, 3 theorems, 113 equations.

Table of Contents

  1. Acknowledgment

Key Result

Theorem 1

Suppose that $F(s) = \sum\limits_{j=1}^{m} c_j L_{j}(s)$ is a linear combination of $m$ distinct Hecke $L$-functions attached to complex ideal class group characters formed with the real coefficients $c_j$. Then a positive proportion of non-trivial zeros of $F(s)$ lie on the critical line. Namely,

Theorems & Definitions (4)

  • Theorem
  • Lemma 1
  • Lemma 2
  • proof