17 papers
Diophantine approximation with sums of two squares II
Stephan Baier, Habibur Rahaman
Recently, the authors showed that for every irrational number , there exist infinitely many positive integers represented by any given positive definite binary quadratic fo…
On certain bilinear sums with modular square roots and applications
Stephan Baier
We extend bounds on additive energies of modular square roots by Dunn, Kerr, Shparlinski, Shkredov and Zaharescu and apply these results to obtain bounds on certain bilinear expone…
Character sums to prime power moduli evaluated at binary quadratic forms
Stephan Baier, Aishik Chattopadhyay
We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character…
Partial progress towards the large sieve for square moduli
Stephan Baier
This paper condenses and expands upon our recent contributions arXiv:2603.00768 and arXiv:2603.25814, which belong together, producing a single streamlined manuscript. We have adde…
A Bombieri-Vinogradov theorem for sectors in real quadratic number fields
Stephan Baier, Esrafil Ali Molla
We establish a Bombieri-Vinogradov theorem for sectors in real quadratic number fields.
On bilinear sums with modular square roots and applications III
Stephan Baier
We continue our investigations of bilinear sums with modular square roots and the large sieve for square moduli in our recent article "On bilinear sums with modular square roots an…