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Andrew Booker introduced a framework to study L-functions through distributions in https://arxiv.org/abs/1308.3067v2. This allowed him and others to get new results about zeros of automorphic L-functions, like the existence of infinitely zeros of $GL(3)$ L-functions of odd order. He also conjectures in https://www.google.com/url?sa=t&source=web&rct=j&url=https://aimath.org/wp-content/uploads/bristol-2018-slides/Booker-talk.pdf&ved=2ahUKEwiZ7LOy9dn1AhV_B2MBHRFRDusQFnoECAoQAQ&usg=AOvVaw1XaYSco54Xx6UmLGN_-yOk the existence of an algebraic structure for the set of L-functions.

Have there been recent developments of this approach leading to new insights about L-functions? Moreover, as the Fourier transform is an automorphism of the Schwartz class, does it give rise to some Fourier transform based symmetry of L-functions?

Andrew Booker introduced a framework to study L-functions through distributions in https://arxiv.org/abs/1308.3067v2. This allowed him and others to get new results about zeros of automorphic L-functions, like the existence of infinitely zeros of $GL(3)$ L-functions of odd order. He also conjectures in this talk the existence of an algebraic structure for the set of L-functions.

Have there been recent developments of this approach leading to new insights about L-functions? Moreover, as the Fourier transform is an automorphism of the Schwartz class, does it give rise to some Fourier transform based symmetry of L-functions?

Andrew Booker, who got widely known for his works on sums of cubes, introduced a framework to study L-functions through distributions in https://arxiv.org/abs/1308.3067v2. This allowed him and others to get new results about zeros of automorphic L-functions, like the existence of infinitely zeros of $GL(3)$ L-functions of odd order. He also conjectures in https://www.google.com/url?sa=t&source=web&rct=j&url=https://aimath.org/wp-content/uploads/bristol-2018-slides/Booker-talk.pdf&ved=2ahUKEwiZ7LOy9dn1AhV_B2MBHRFRDusQFnoECAoQAQ&usg=AOvVaw1XaYSco54Xx6UmLGN_-yOk the existence of an algebraic structure for the set of L-functions.

Have there been recent developments of this approach leading to new insights about L-functions? Moreover, as the Fourier transform is an automorphism of the Schwartz class, does it give rise to some Fourier transform based symmetry of L-functions?

Andrew Booker introduced a framework to study L-functions through distributions in https://arxiv.org/abs/1308.3067v2. This allowed him and others to get new results about zeros of automorphic L-functions, like the existence of infinitely zeros of $GL(3)$ L-functions of odd order. He also conjectures in https://www.google.com/url?sa=t&source=web&rct=j&url=https://aimath.org/wp-content/uploads/bristol-2018-slides/Booker-talk.pdf&ved=2ahUKEwiZ7LOy9dn1AhV_B2MBHRFRDusQFnoECAoQAQ&usg=AOvVaw1XaYSco54Xx6UmLGN_-yOk the existence of an algebraic structure for the set of L-functions.

Have there been recent developments of this approach leading to new insights about L-functions? Moreover, as the Fourier transform is an automorphism of the Schwartz class, does it give rise to some Fourier transform based symmetry of L-functions?

Andrew Booker, who got widely known for his works on sums of cubes, introduced a framework to study L-functions through distributions in https://arxiv.org/abs/1308.3067v2. This allowed him and others to get new results about zeros of automorphic L-functions, like the existence of infinitely zeros of $GL(3)$ L-functions of odd order. He also conjectures in https://www.google.com/url?sa=t&source=web&rct=j&url=https://aimath.org/wp-content/uploads/bristol-2018-slides/Booker-talk.pdf&ved=2ahUKEwiZ7LOy9dn1AhV_B2MBHRFRDusQFnoECAoQAQ&usg=AOvVaw1XaYSco54Xx6UmLGN_-yOk the existence of an algebraic structure for the set of L-functions.

Have there been recent developments of this approach leading to new insights about L-functions?

Andrew Booker, who got widely known for his works on sums of cubes, introduced a framework to study L-functions through distributions in https://arxiv.org/abs/1308.3067v2. This allowed him and others to get new results about zeros of automorphic L-functions, like the existence of infinitely zeros of $GL(3)$ L-functions of odd order. He also conjectures in https://www.google.com/url?sa=t&source=web&rct=j&url=https://aimath.org/wp-content/uploads/bristol-2018-slides/Booker-talk.pdf&ved=2ahUKEwiZ7LOy9dn1AhV_B2MBHRFRDusQFnoECAoQAQ&usg=AOvVaw1XaYSco54Xx6UmLGN_-yOk the existence of an algebraic structure for the set of L-functions.

Have there been recent developments of this approach leading to new insights about L-functions? Moreover, as the Fourier transform is an automorphism of the Schwartz class, does it give rise to some Fourier transform based symmetry of L-functions?