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The Resource Analytic Number Theory : In Honor of Helmut Maier's 60th Birthday

Analytic Number Theory : In Honor of Helmut Maier's 60th Birthday

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Analytic Number Theory : In Honor of Helmut Maier's 60th Birthday
Title
Analytic Number Theory
Title remainder
In Honor of Helmut Maier's 60th Birthday
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Subject
Language
eng
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MiAaPQ
Literary form
non fiction
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dictionaries
Analytic Number Theory : In Honor of Helmut Maier's 60th Birthday
Label
Analytic Number Theory : In Honor of Helmut Maier's 60th Birthday
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http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4097998
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Contents -- CM-Points on Straight Lines -- 1 Introduction -- 2 Imaginary Quadratic Orders -- 2.1 Class Groups -- 2.2 Orders with Class Groups Annihilated by 2 -- 3 Ring Class Fields and Complex Multiplication -- 3.1 Compositum of Ring Class Fields -- 3.2 Complex Multiplication -- 3.3 The Conjugates of j(x) -- 4 Comparing Two CM-Fields -- 4.1 The Case Q(x1)Q(x2) -- 4.2 The Case Q(x1)= Q(x2) -- 5 Proof of Theorem 1.2 -- 5.1 Both Coordinates are Dominant -- 5.2 Completing the Proof -- References -- Maass Waveforms and Low-Lying Zeros -- 1 Introduction -- 1.1 Zeros of L-Functions -- 1.2 n-Level Correlations and Random Matrix Theory -- 1.3 n-Level Densities and the Katz-Sarnak Philosophy -- 2 Statement of Main Results -- 2.1 Normalizations and Notation -- 2.2 Main Results -- 2.3 Outline of Arguments -- 3 Preliminaries for the Proofs -- 3.1 Calculating the Averaged One-Level Density -- 3.2 Handling the Bessel Integral -- 4 Proofs of the Main Theorems -- 4.1 Proof of Theorem 2.2 -- 4.2 Proof of Theorem 2.3 -- 4.3 Proof of Theorem 2.4 -- 4.4 Proof of Theorem 2.5 -- Appendix 1: Contour Integration -- Appendix 2: An Exponential Sum Identity -- Appendix 3: 2-Level Calculations -- References -- Théorème de Jordan Friable -- 1 Introduction et énoncé des résultats -- 2 Preuve du Théorème 1.1 -- 3 Preuve du Théorème 1.2 -- Bibliographie -- On Conjectures of T. Ordowski and Z.W. Sun Concerning Primes and Quadratic Forms -- 1 Primes and Quadratic Forms -- 2 Proofs: The Simplest Case -- 3 Proofs: The General Positive Definite Case -- 4 The Indefinite Case -- References -- Large Gaps Between Consecutive Prime Numbers Containing Perfect Powers -- 1 Introduction -- 2 Sieve Estimates -- 3 kth Power Residues and Prime Ideals -- 4 Main Argument -- References -- On the Parity of the Number of Small Divisors of n -- 1 Introduction -- 2 Proof of Theorem 1.1
  • 3 A Corollary -- 4 Final Thoughts -- References -- Counting Primes in Arithmetic Progressions -- 1 Primes in an Individual Progression -- 2 Approaching Twin Primes with the Sieve -- 3 Primes in an Arithmetic Progression, on Average -- 4 Maier's Idea -- 5 Bilinear Forms and the BFI Conjectures -- 6 B-V Type Theorems with Special Weights -- References -- Limit Points of the Sequence of Normalized Differences Between Consecutive Prime Numbers -- 1 Introduction -- 2 Erdős's Method -- 3 Proof of the Lemmas -- 4 Further Results and Comments -- References -- Spirals of the Zeta Function I -- 1 Introduction -- 2 Proof of the Theorem -- References -- Best Possible Densities of Dickson m-Tuples, as a Consequence of Zhang-Maynard-Tao -- 1 Introduction and Statement of Results -- 2 The Density of de Polignac Numbers -- 3 Proof of Theorem 1.1 -- 4 The Number Of Admissible k-Tuples -- 5 A Better Density in the Continuous Case -- References -- A Note on Helson's Conjecture on Moments of Random Multiplicative Functions -- 1 Introduction -- 2 Lower Bounds for the First Moment -- 2.1 Proof of Proposition 2.1 -- 2.2 Proofs of Theorem 1.1 and Proposition 2.2 -- 3 Lower Bounds for small Moments: Proof of Theorem 1.2 -- 4 Asymptotics for Even Moments: Proof of Theorem 1.3 -- 5 Proof of Theorem 1.4 -- References -- Large Values of the Zeta-Function on the Critical Line -- 1 The Basic Properties of i(s) -- 1.1 The Definitions -- 1.2 The Selberg Class -- 2 Moments on the 1/2-Line -- 2.1 Basic Concepts -- 2.2 Lower Bounds for i(12+it) in Short Intervals -- 2.3 Upper Bounds for i(12+it) in Short Intervals Under the RH -- 3 The Conjectural Formula for Ik(T) -- 4 The Large Values Technique for Zeta-Sums -- 4.1 Introduction -- 4.2 The Large Values Technique -- 5 Atkinson's Formula for the Mean Square -- 6 The 12th Moment Estimate -- 6.1 Technical Preparation
  • 6.2 Reduction to Exponential Sums -- 7 Large Values of
  • References -- On the Ratio of Consecutive Gaps Between Primes -- 1 Introduction -- (A) Large Gaps Between Primes (Until August 2014) -- (A*) Very Recent Developments Concerning Large Gaps Between Primes -- (B) Chains of Large Gaps Between Consecutive Primes -- (C) Small Gaps Between Consecutive Primes -- (D) Chains of Bounded Gaps Between Consecutive Primes -- 2 Consecutive Values of dn: Problems of Erdős, Turán, and Pólya -- 3 Results -- 4 Proofs -- References -- Remarks on Fibers of the Sum-of-Divisors Function -- 1 Introduction -- 1.1 Notation -- 2 Proof of Theorem 1.1 -- 3 Proof of Theorem 1.2 -- 3.1 Overview of the Basic Method -- 3.2 Definition of the Set Av -- 3.3 The Proof Proper -- 3.3.1 Rewriting v(a)=v(a') -- 3.3.2 The Key Sieve Lemma -- 3.3.3 Capturing Solutions with Lemma 3.2: Attempt #1 -- 3.3.4 Attempt #2 -- 3.3.5 Finishing Up -- 4 Proof of Corollary 1.1 -- References -- On Amicable Numbers -- 1 Introduction -- 2 A Lemma -- 3 Proof of Theorem 1.1 -- References -- Trigonometric Representations of Generalized Dedekind and Hardy Sums via the Discrete Fourier Transform -- 1 Introduction -- 2 Properties of the DFT -- 3 Applications -- 3.1 Generalized Dedekind Sums -- 3.2 Generalized Hardy Sums -- 3.3 Sums Involving the Hurwitz Zeta Function -- 4 Some Further Remarks -- References -- On Arithmetic Properties of Products and Shifted Products -- 1 Introduction -- 2 The Sum of Digits of Products ab -- 3 Proof of Theorem 2.1 -- 4 Squarefree Shifted Products -- 5 Proof of Theorem 4.2 -- References -- Narrow Progressions in the Primes -- 1 Introduction -- 1.1 Previous Results -- 1.2 Main New Result -- 2 Preliminary Reductions -- 3 The Enveloping Sieve -- 4 Averaged Local Gowers Norms -- 5 The Dense Model Theorem -- 6 Densification -- 7 The Linear Case -- References
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1 online resource (378 pages)
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online
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9783319222400
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rdamedia
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