3 papers
math.NT2024
Averages of arithmetic functions over polynomials in many variables
Kevin Destagnol, Efthymios Sofos
We estimate the average of any arithmetic function over the values of any smooth polynomial in many variables provided only that has a distribution in arithmetic progressio…
math.NT2024
Diophantine stability and second order terms
Carlo Pagano, Efthymios Sofos
We establish a Galois-theoretic trichotomy governing Diophantine stability for genus curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine s…
math.NT2024
Averages of multiplicative functions along equidistributed sequences
Stephanie Chan, Peter Koymans, Carlo Pagano +1
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.