Zeros of L-functions outside the critical strip

Andrew R. Booker; Frank Thorne

doi:10.2140/ant.2014.8.2027

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arXiv · 1306.6362

Zeros of L-functions outside the critical strip

Andrew R. Booker·Frank Thorne

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Abstract

For a wide class of Dirichlet series associated to automorphic forms, we show that those without Euler products must have zeros within the region of absolute convergence. For instance, we prove that if f is a classical holomorphic modular form whose L-function does not vanish for Re(s) > (k+1)/2, then f is a Hecke eigenform. Our proof adapts and extends work of Saias and Weingartner, who proved a similar result for degree 1 L-functions.

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BibTeX RIS

Andrew R. Booker, Frank Thorne. 2018-06-18. Zeros of L-functions outside the critical strip. https://doi.org/10.2140/ant.2014.8.2027

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