All Outputs (6)

Large sums of high‐order characters (2023)
Journal Article
Mangerel, A. P. (2024). Large sums of high‐order characters. Journal of the London Mathematical Society, 109(1), Article e12841. https://doi.org/10.1112/jlms.12841

Let χ $\chi$ be a primitive character modulo a prime q $q$ , and let δ > 0 $\delta > 0$ . It has previously been observed that if χ $\chi$ has large order d ⩾ d 0 ( δ ) $d \geqslant d_0(\delta)$ then χ ( n ) ≠ 1 $\chi (n) \ne 1$ for some n ⩽ q δ $... Read More about Large sums of high‐order characters.

Three conjectures about character sums (2023)
Journal Article
Granville, A., & Mangerel, A. P. (2023). Three conjectures about character sums. Mathematische Zeitschrift, 305(3), Article 49. https://doi.org/10.1007/s00209-023-03374-8

We establish that three well-known and rather different looking conjectures about Dirichlet characters and their (weighted) sums, (concerning the Pólya–Vinogradov theorem for maximal character sums, the maximal admissible range in Burgess’ estimate f... Read More about Three conjectures about character sums.

Beyond the Erdős discrepancy problem in function fields (2023)
Journal Article
Klurman, O., Mangerel, A. P., & Teräväinen, J. (2024). Beyond the Erdős discrepancy problem in function fields. Mathematische Annalen, 389(3), 2959-3008. https://doi.org/10.1007/s00208-023-02700-z

We characterize the limiting behavior of partial sums of multiplicative functions f:Fq[t]→S1. In contrast to the number field setting, the characterization depends crucially on whether the notion of discrepancy is defined using long intervals, short... Read More about Beyond the Erdős discrepancy problem in function fields.

Multiplicative functions in short arithmetic progressions (2023)
Journal Article
Klurman, O., Mangerel, A. P., & Teräväinen, J. (2023). Multiplicative functions in short arithmetic progressions. Proceedings of the London Mathematical Society, 127(2), 366-446. https://doi.org/10.1112/plms.12546

Sign changes of fourier coefficients of holomorphic cusp forms at norm form arguments (2023)
Journal Article
MANGEREL, A. P. (2023). Sign changes of fourier coefficients of holomorphic cusp forms at norm form arguments. Mathematical Proceedings of the Cambridge Philosophical Society, https://doi.org/10.1017/s0305004123000294

Divisor-bounded multiplicative functions in short intervals (2023)
Journal Article
Mangerel, A. P. (2023). Divisor-bounded multiplicative functions in short intervals. Research in the Mathematical Sciences, 10(12), https://doi.org/10.1007/s40687-023-00376-0

We extend the Matomäki–Radziwiłł theorem to a large collection of unbounded multiplicative functions that are uniformly bounded, but not necessarily bounded by 1, on the primes. Our result allows us to estimate averages of such a function f in typica... Read More about Divisor-bounded multiplicative functions in short intervals.