Real zeros of quadratic Dirichlet L-functions

By J. Brian Conrey, Kannan Soundararajan. 2001

51 citations recorded by the source corpus.

We show that for a positive proportion of real primitive Dirichlet characters chi, the associated Dirichlet L-function L(s,chi) has no zeros on the positive real axis. Prior to this it was not known whether or not there were infinitely many L-functions (from any family) with no positive real zeros.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4c61be83262878f20c4681f361c6d889d37b523c

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Mathematical Physics

Citations in the corpus

Sign changes of coefficients of half integral weight modular forms (2007, background): “and Soundararajan [ CS ], Chowla’s conjecture is true for a positive proportion of positive square-free integers t. If f is a Hecke eigenform, we can in fact prove an unconditional and much better result on the sign changes of the sequence (a(tp 2m ))m∈N where p is a prime”
Applications of the L‐functions ratios conjectures (2005, background): “Examples of second moment mollifying in a symplectic family occur in [40] and [15].”
Extreme values of zeta and L-functions (2007, background): “From [13] we know that L( 1 2 , χd) 6= 0 for a large proportion (78 ) of fundamental discriminants d, and from [3] that L( 1 2 , χd) > 0 for a positive proportion of fundamental discriminants d.”