Essays in Analytic Number Theory

This book offers a comprehensive exploration of cutting-edge research in Analytic Number Theory, celebrating the profound contributions of Helmut Maier on his 70th birthday. With chapters penned by leading mathematicians from around the globe, this volume presents state-of-the-art findings and insights into a wide array of topics within the field. Readers will encounter in-depth studies on subjects such as random matrix models for cusp forms, the Chevalley-Bass theorem, and Weierstrass Fractal Drums. The book also delves into the $L_q$ norm of Rudin-Shapiro polynomials, shifted-prime divisors, and sharp local estimates for smooth numbers. Further, it examines the invariants of $L$-functions, an analogue of the Mertens function, the Riemann Hypothesis zeta function, Dirichlet polynomials and exponential sums. This collection is an invaluable resource for graduate students and seasoned researchers in Analytic Number Theory and related disciplines. It not only honors Maier's groundbreaking work but also serves as a beacon for future research, offering insights and methodologies that will inspire continued exploration and discovery in the field.