Our group employs advanced analytic techniques to explore the distribution of prime numbers, the behavior of multiplicative functions, and the arithmetic of special values of L-functions. Particular attention is given to multiple zeta values and their generalizations, including multiple Apéry-like sums. We study explicit averages beyond classical asymptotic bounds and examine Möbius function summations under refined coprimality constraints, advancing techniques in additive number theory as well.
A significant aspect of our work involves the Beurling–Selberg extremal function and its applications in bounding prime-counting error terms. We also develop novel approaches to bounding the tails of multiple zeta value series, investigating their structural connections with algebraic and combinatorial frameworks. These efforts reflect our broader goal of connecting analytic number theory with modern structures in arithmetic geometry and combinatorics.