L-functions as distributions

Abstract

We define an axiomatic class of L-functions extending the Selberg class. We show in particular that one can recast the traditional conditions of an Euler product, analytic continuation and functional equation in terms of distributional identities akin to Weil's explicit formula. The generality of our approach enables some new applications; for instance, we show that the L-function of any cuspidal automorphic representation of GL_3(A_Q) has infinitely many zeros of odd order.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00208-015-1178-z

References in corpus (2)

• Detecting squarefree numbers
• Zeros of L-functions outside the critical strip

Cited by in corpus (9)

• L-series of harmonic Maass forms and a summation formula for harmonic lifts
• Beyond the extended Selberg class: $d_F\le 1$
• Weil's converse theorem for Maass forms and cancellation of zeros
• A converse theorem without root numbers
• Ratios of Artin L-functions
• Conductor zeta function for the GL(2) universal family
• Hamiltonians arising from L-functions in the Selberg class
• Notes on Low Degree L-Data
• Murmurations of modular forms in the weight aspect