Essays in Analytic Number Theory by Friedlander, John; Pomerance, Carl; Rassias, Michael Th.;

Hosszú leírás:

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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.

Tartalomjegyzék:

Preface.- A survey of a random matrix model for a family of cusp forms.- The Chevalley-Bass Theorem.- Weierstrass Fractal Drums - II Towards a Fractal Cohomology.- The Lq norm of the Rudin-Shapiro polynomials on subarcs of the unit circle.- Shifted-prime divisors.- Sharp local estimates for smooth numbers.- On the invariants of L-functions of degree 2, II: twisted conductor.- An analogue of Mertens function for Rankin-Selberg L-function Lf×f (s).- An effective Linear Independence conjecture for the zeros of the Riemann zeta function and applications.- A note on zero density results implying large value estimates for Dirichlet polynomials.- A mean square minorant for exponential sums.- Extremal problems and the combinatorics of sumsets.- Distribution of Goldbach numbers in short intervals. Mikawa’s problem.- Counting rational points on some affine surfaces.- On partial derivatives of some summatory functions.- Cyclotomic statistics.- A Picture Book of the Riemann Hypothesis or Destructive Interference in Quantum Theory, Lines of Constant Phase and Height, and the Riemann Hypothesis.- The generalized Montgomery-Hooley formula: A survey.