Zeros of GL2 𝐿-functions on the critical line-Reference-Cited by-同舟云学术

Zeros of GL2 𝐿-functions on the critical line

Author:

Andersen Nickolas¹,Thorner Jesse²

Affiliation:

1. Department of Mathematics , Brigham Young University , Provo , USA

2. Department of Mathematics , University of Illinois (Urbana-Champaign) , Urbana , USA

Abstract

Abstract We use Levinson’s method and the work of Blomer and Harcos on the GL 2

\mathrm{GL}_{2}

shifted convolution problem to prove that at least 6.96 % of the nontrivial zeros of the 𝐿-function of a GL 2

\mathrm{GL}_{2}

automorphic form lie on the critical line.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

Reference22 articles.

1. D. Bernard, Statistics on non-trivial zeros of modular L-functions, Thesis, University Blaise Pascal - Clermont-Ferrand II, 2013.

2. D. Bernard, Modular case of Levinson’s theorem, Acta Arith. 167 (2015), no. 3, 201–237.

3. V. Blomer, Rankin–Selberg 𝐿-functions on the critical line, Manuscripta Math. 117 (2005), no. 2, 111–133.

4. V. Blomer and F. Brumley, On the Ramanujan conjecture over number fields, Ann. of Math. (2) 174 (2011), no. 1, 581–605.

5. V. Blomer and G. Harcos, The spectral decomposition of shifted convolution sums, Duke Math. J. 144 (2008), no. 2, 321–339.

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