Irregularities in the distribution of prime numbers : from the era of Helmut Maier's matrix method and beyond /: from the era of Helmut Maier's matrix method and beyond. ([2018])

• Record Type: Book
• Further Information: Note: János Pintz, Michael Th. Rassias, editors.
• Editors: Pintz, János; Rassias, Michael Th, 1987-
• Contents: Intro; Foreword; References; Preface; Contents; Chains of Large Gaps Between Primes; 1 Introduction; 1.1 Notational Conventions; 2 Siegel Zeroes; 3 Sieving an Interval; 4 Sieving a Set of Primes; 5 Using a Hypergraph Covering Theorem; 6 Using a Sieve Weight; References; A Note on the Distribution of Primes in Intervals; 1 Introduction; 2 Some Literature; 2.1 The Singular Series on Average; 2.2 Unconditional Results; 3 Notation; 4 Ancillary Results; 4.1 Inclusion-Exclusion; 4.2 The Singular Series, As a Series; 4.3 The Singular Series, on Average; 5 Main Results; 6 Concluding Remarks On the Difference in Values of the Euler Totient FunctionNear Prime Arguments1 Introduction; 2 Proof of Theorem 1 for = 1; 2.1 The Case of Equality; 2.2 A Comparison Lemma; 2.3 Some Preliminaries; 2.4 Inconvenient Primes of Type 1; 2.5 Inconvenient Primes of Type 2; 2.6 Inconvenient Primes of Type 3; 2.7 Inconvenient Primes of Type 4; 2.8 Convenient Primes; 2.9 Weird Primes; 2.10 Conclusion; 2.11 Sanity Check; 3 Proof of Theorem 1 for 2; 3.1 The Case of Equality; 3.2 A More General Comparison Lemma; 3.3 Final Ingredient; References Vinogradov's Mean Value Theorem as an Ingredient in Polynomial Large Sieve Inequalities and Some Consequences1 Introduction; 2 Overview of Current Polynomial LSI Bounds and Conjectures; 3 The Path from VMVT to Polynomial Large Sieve Inequalities; 4 Fraction Counting: Bounds for the Spacing Problem; 5 Consequences of the Polynomial LSI for the Distribution of Primes in Certain Arithmetic Progressions; References; Unexpected Regularities in the Behavior of Some Number-Theoretic Power Series; 1 Introduction; 2 Fake Asymptotics and the Fröberg Heuristic; 3 Better than Expected Error Terms 4 Fake Asymptotics for Other Number-Theoretic Power Series4.1 Möbius Series with ``Scaled'' Coefficients; 4.2 Möbius Series with Non-principal Characters; 4.3 Möbius Series with Coprimality Condition; 4.4 The Liouville Power Series; 5 Concluding Remarks; References; The Convex Hull of the Prime Number Graph; 1 Introduction; 2 Counting the Convex Primes; 3 Edge Convex Primes; 4 Multiplicatively Convex Primes; 5 Data and Future Work; References; Irregular Behaviour of Class Numbers and Euler-Kronecker Constants of Cyclotomic Fields: The Log Log Log Devil at Play; 1 Introduction
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource
• Subjects: 512.72; Mathematics; Numbers, Prime; MATHEMATICS / Algebra / Intermediate; Numbers, Prime; Mathematics; Number Theory; Functions of a Complex Variable; Special Functions; Mathematics -- Mathematical Analysis; Complex analysis, complex variables; Functional analysis & transforms; Number theory; Functions of complex variables; Functions, special; Mathematics -- Number Theory; Number theory; Electronic books
• Languages: English
• ISBNs: 9783319927770; 3319927779; 3319927760; 9783319927763
• Related ISBNs: 9783319927763; 3319927760
• Notes: Note: Includes bibliographical references.; Note: Vendor-supplied metadata.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.