Essays in Analytic Number Theory
Description
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.
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Persons
John Friedlander is University Professor Emeritus (Mathematics) at the University of Toronto. He received his B.Sc. from the University of Toronto in 1965, an M.A. from the University of Waterloo in 1966, and a Ph.D. from Pennsylvania State University in 1972. He was a lecturer at M.I.T. in 1974-76 and has been on the faculty of the University of Toronto since 1977, where he served as Chair of Mathematics during 1987-91. He has also spent several years at the Institute for Advanced Study. He has been bestowed with the Jeffery-Williams Prize, the CRM-Fields Prize and (joint with H. Iwaniec) the Joseph L. Doob Prize. He is a Fellow of the Royal Society of Canada as well as a Fellow of the American Mathematical Society, the Canadian Mathematical Society and the Fields Institute.
Carl Pomerance is a Professor Emeritus at the Department of Mathematics of Dartmouth College. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least seven distinct prime factors. He joined the faculty at the University of Georgia, becoming a full professor in 1982. He subsequently worked at Lucent Technologies for a number of years and then became a Professor at Dartmouth College. He has been bestowed with several awards, including the Chauvenet Prize in 1985, the Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics in 1997, and the Levi L. Conant Prize in 2001. In 2012 he became a fellow of the American Mathematical Society. He also became the John G. Kemeny Parents Professor of Mathematics in the same year.
Michael Th. Rassias is a Professor at the Department of Mathematics and Engineering Sciences of the Hellenic Military Academy. He obtained his PhD in Mathematics from ETH-Zürich in 2014. For the period 2015-2021 he was a researcher with teaching duties at the Institute of Mathematics of the University of Zürich and for the period 2015-2023, he was a visiting researcher at the Program in Interdisciplinary Studies of the Institute for Advanced Study, Princeton. Additionally, during the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F. Nash, Jr. (Nobel Prize, 1994 and Abel Prize, 2015) the volume Open Problems in Mathematics , Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo.
Content
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.