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Analytic Number Theory, Modular Forms and q-Hypergeometric Series

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Cover of 'Analytic Number Theory, Modular Forms and q-Hypergeometric Series'

Table of Contents

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    Book Overview
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    Chapter 1 Plus-Minus Weighted Zero-Sum Constants: A Survey
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    Chapter 2 Vector-valued Modular Forms and the Seventh Order Mock Theta Functions
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    Chapter 3 The Alladi–Schur Polynomials and Their Factorization
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    Chapter 4 New Representations for $$\sigma (q)$$ via Reciprocity Theorems
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    Chapter 5 Mean Values of the Functional Equation Factors at the Zeros of Derivatives of the Riemann Zeta Function and Dirichlet L -Functions
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    Chapter 6 New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions
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    Chapter 7 The Appearance of H.F. Baker and E.W. Hobson in “The Man Who Knew Infinity”
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    Chapter 8 A Bibasic Heine Transformation Formula and Ramanujan’s $$_2\phi _1$$ Transformations
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    Chapter 9 Adventures with the OEIS
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    Chapter 10 Three-Colored Partitions and Dilated Companions of Capparelli’s Identities
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    Chapter 11 Nearly Equal Distributions of the Rank and the Crank of Partitions
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    Chapter 12 Holonomic Alchemy and Series for $$1/\pi $$
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    Chapter 13 Integral Points on a Very Flat Convex Curve
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    Chapter 14 Unification, Refinements and Companions of Generalisations of Schur’s Theorem
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    Chapter 15 Integrals Involving Rudin–Shapiro Polynomials and Sketch of a Proof of Saffari’s Conjecture
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    Chapter 16 From Ramanujan to Groups of Rationals: A Personal History of Abstract Multiplicative Functions
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    Chapter 17 On an Additive Prime Divisor Function of Alladi and Erdős
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    Chapter 18 Ramanujan’s Tau Function
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    Chapter 19 Construction of Cusp Forms Using Rankin–Cohen Brackets
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    Chapter 20 An Open Problem of Corteel, Lovejoy, and Mallet
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    Chapter 21 On the Asymptotics of Partial Theta Functions
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    Chapter 22 Overpartitions and Truncated Partition Identities
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    Chapter 23 Congruences Modulo Powers of 2 for the Number of Unique Path Partitions
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    Chapter 24 Complex Form of Classical and Quantum Electrodynamics
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    Chapter 25 On a System of q -Partial Differential Equations with Applications to q -Series
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    Chapter 26 Asymmetric Generalizations of Schur’s Theorem
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    Chapter 27 Local Behavior of the Composition of the Aliquot and Co-Totient Functions
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    Chapter 28 On the Universal Mock Theta Function $$g_{{{\scriptstyle 2}}}$$ and Zwegers’ $$\mu $$ -Function
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    Chapter 29 Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series
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    Chapter 30 Littlewood Polynomials
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    Chapter 31 Trapezoidal Numbers, Divisor Functions, and a Partition Theorem of Sylvester
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    Chapter 32 Estimates of $${{\mathrm{li}}}(\theta (x))-\pi (x)$$ and the Riemann Hypothesis
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    Chapter 33 Partition-Theoretic Formulas for Arithmetic Densities
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    Chapter 34 A New Witness Identity for $$\varvec{11\mid p(11n+6)}$$
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    Chapter 35 On the Representations of a Positive Integer by Certain Classes of Quadratic Forms in Eight Variables
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    Chapter 36 A Note on Thue Inequalities with Few Coefficients
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    Chapter 37 Basic Hypergeometric Summations from Rook Theory
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    Chapter 38 Overpartitions and Singular Overpartitions
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    Chapter 39 A classical $q$-hypergeometric approach to the standard $A_2^{(2)}$ standard modules
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    Chapter 40 Generalized Mertens Sums
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Title
Analytic Number Theory, Modular Forms and q-Hypergeometric Series
Published by
Springer International Publishing, February 2018
DOI 10.1007/978-3-319-68376-8
ISBNs
978-3-31-968375-1, 978-3-31-968376-8
Editors

Andrews, George E., Garvan, Frank

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