When the eggs are fried

2:00pm, Wednesday 15 October 2025

Abstract

Grey, dear friends, is all unproven theory.  Thus I mar the immortal words of a very witty and most unjustly abused immortal.  At the most recent meeting of Number Theory Down Under, it was suggested that the work of Kerr-Shparlinski-Wu-Xi on Kloosterman sums might be applied to improve an asymptotic formula of Gao-Zhao for the twisted fourth moment of Dirichlet L-functions to certain prime power moduli, as this latter result was presented.  Can this idea work?  We heeded Sancho Panza's counsel that "you'll see when the eggs are fried" and greened the untested theory.  More specifically, taking the above recommendation, as well as doing other things, we extended the aforesaid moment result to general moduli and significantly improved the error term.  I shall report on this recent work (arXiv:2509.24690), joint with P. Gao and X. Wu, during this talk.