4 papers
Muon: Muon with Fractional Spectral Powers
Yihe Dong, Will Sawin
Muon is an increasingly widely used optimizer that replaces a gradient with its polar factor , thereby flattening the singular spectrum. However, full flatten…
Bilinear forms with trace functions
Ãtienne Fouvry, Emmanuel Kowalski, Philippe Michel +1
We obtain non-trivial bounds for bilinear sums of trace functions below the Pólya-Vinogradov range assuming only that the geometric monodromy group of the underlying ell-adic shea…
Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
E. Kowalski, Ph. Michel, W. Sawin
We prove non-trivial bounds for bilinear forms with hyper-Kloosterman sums with characters modulo a prime which, for both variables of length , are non-trivial as soon as $M…
The Shafarevich conjecture for hypersurfaces in abelian varieties
Brian Lawrence, Will Sawin
Faltings proved that there are finitely many abelian varieties of genus over a number field , with good reduction outside a finite set of primes . Fixing one of these abe…