Number Theory in Memory of Eduard Wirsing

ISBN-13: 9783031316166 / Angielski

Helmut Maier; Jörn Steuding; Rasa Steuding

Opis

Eduard Wirsing was an outstanding number theorist. In his research he made significant contributions to various subfields of number theory and also published together with other eminent scientists (e.g., with the Fields Medalist Alan Baker as well as Don Zagier). The commemorative volume will include numerous number-theoretic papers on current research by well-known representatives as well as some personal recollections by companions of Wirsing.

The topics range from arithmetical functions, continued fractions, elementary proofs of the prime number theorem, friable integers, the Goldbach problem, Dirichlet series, Euler products and more to personal reminiscences. There is something for every interested reader.

Spis treści

Life and Work of Eduard Wirsing.- Remembering Eduard Wirsing.- Personal Memories.- On the Infimum of the Absolute Value of Successive Derivatives of a Real Function Defined on a Bounded Interval.- Friable Averages of Oscillating Arithmetic Functions.- Ein quaternäres Waring-Goldbach-Problem.- Coprimality of Consecutive Elements in a Piatetski-Shapiro Sequence.- Wirsing’s Elementary Proofs of the Prime Number Theorem with Remainder Terms.- Diophantine Analysis Around .[1, 2, 3, . . . ].- On a Smoothed Average of the Number of Goldbach Representations.- Estimates for k-Dimensional Spherical Summations of Arithmetic Functions of the GCD and LCM.- The Rational Points Close to a Space Curve.- Twists by Dirichlet Characters and Polynomial Euler Products of L-Functions, II.- Solving the Iterative Differential Equation .−γgt = g−1.- Irrationality of Zeros of the Digamma Function.- Generalizations of Menon’s Arithmetic Identity.- On a Conjecture of Descartes.- On the Greatest Common Divisor of a Number and Its Sum of Divisors, II.- Permutations with Arithmetic Constraints.- Large Subsums of the Möbius Function.- The a-Points of the Riemann Zeta-Function and the Functional Equation.- Braided Gibonacci Sequences on Residue Classes.

O autorze

Helmut Maier was born in Geislingen/Steige, Germany, on October 17, 1953. He graduated with a Diploma in Mathematics from the University of Ulm under the supervision of Professor H.E.Richert. After a period as a scientific employee he started his doctoral studies at the University of Minnesota and received his Ph.D. in 1981 under the supervision of Professor J.Ian Richards. After postdoctoral positions at the University of Michigan and the Institute for Advanced Studies he accepted a tenure track position at the University of Georgia, where he collaborated with Professor Carl Pomerance. In 1993  he accepted a position as a Professor at the University of Ulm. Since 2019 he is retired and has a position as a Senior Professor at the University of Ulm.

Jörn Steuding (*1969) studied and received his doctorate in Hanover in 1999, habilitated in Frankfurt am Main in 2004 and was subsequently investigador Ramón y Cajal at the Universidad Autónoma de Madrid. Since 2006 he is professor of number theory at the University of Würzburg. His research deals mostly with topics in analytic number theory; however, there is also interest in cryptography, graph theory and the history of mathematics.

Rasa Steuding (*1975) studied and received her doctorate in Vilnius in 2002, and was subsequently a lecturer in Siauliai, a postdoc at the Universidad Autónoma de Madrid, and a lecturer at the RheinMain University of Applied Sciences. Her research interests are analytic number theory and cryptography. Since 2006 she is associated with the number theory group at Würzburg.

Blurb

Eduard Wirsing was an outstanding number theorist. In his research he made significant contributions to various subfields of number theory and also collaborated with other eminent scientists (e.g., with the Fields Medalist Alan Baker as well as Don Zagier). This commemorative volume includes numerous papers on current research in number theory by well-known experts, as well as some personal recollections by companions of Wirsing.

The topics covered in this volume include arithmetical functions, continued fractions, elementary proofs of the prime number theorem, friable integers, the Goldbach problem, Dirichlet series, Euler products, and more. There is something for every interested reader.