02204cam a22003018i 450000100090000000300040000900500170001300800410003001000170007102000300008804000230011804200080014105000230014908200180017210000400019024501200023026300090035030000140035949000530037350400510042652010290047765000330150677601780153990600450171794200120176295201110177499900170188521907471OSt20230829185834.0210217s2021 enk b 001 0 eng a 2021002811 a9781108840965q(hardback) aDLCbengerdacDLC apcc00aQA241.7b.K69 202100a512.7 KOW2231 aKowalski, Emmanuel,d1969-eauthor.13aAn introduction to probabilistic number theory /cEmmanuel Kowalski, Swiss Federal Institute of Technology, Zurich. a2104 apages cm.0 aCambridge studies in advanced mathematics ;v192 aIncludes bibliographical references and index. a"Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years, the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums, and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis, and probability, making it a readable and incisive introduction to this beautiful area of mathematics"-- 0aProbabilistic number theory.08iOnline version:aKowalski, Emmanuel, 1969-tAn introduction to probabilistic number theoryb1.dNew York : Cambridge University Press, 2021.z9781108888226w(DLC) 2021002812 a7bcbccorignewd1eecipf20gy-gencatlg 2ddccBK 00102ddc4052708BKaSTPbSTPcNBd2023-08-29l0o512.7 KOWp11647r2023-08-29 00:00:00w2023-08-29yBK c21577d21577