On the generalised Dirichlet divisor problem
Speaker: Chiara Bellotti
Date: Thu, Jun 20, 2024
Location: PIMS, University of British Columbia
Conference: Comparative Prime Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Thu, Jun 20, 2024
Location: PIMS, University of British Columbia
Conference: Comparative Prime Number Theory
Subject: Mathematics, Number Theory
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
In this talk we present new unconditional estimates on $\Delta k(x)$, the remainder term associated with the generalised divisor function, for large $k$. By combining new estimates of exponential sums and Carlson’s exponent, we show that $\Delta k(x) \ll x^{1−1.224(k−2.36)^{−2/3}}$ for $k \geq 58$ and $\Delta k(x) \ll x^{1−1.889k^{−2/3}}$ for all sufficiently large fixed $k$. This is joint work with Andrew Yang.
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