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Analytic Number Theory, Modular Forms and q-Hypergeometric Series

Overview of attention for book
Cover of 'Analytic Number Theory, Modular Forms and q-Hypergeometric Series'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    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
Attention for Chapter 12: Holonomic Alchemy and Series for $$1/\pi $$
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Chapter title
Holonomic Alchemy and Series for $$1/\pi $$
Chapter number 12
Book title
Analytic Number Theory, Modular Forms and q-Hypergeometric Series
Published in
arXiv, March 2016
DOI 10.1007/978-3-319-68376-8_12
Book ISBNs
978-3-31-968375-1, 978-3-31-968376-8
Authors

Shaun Cooper, Wadim Zudilin, James G. Wan, Cooper, Shaun, Wan, James G., Zudilin, Wadim

View on publisher site
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 Attention Score in Context

Attention Score in Context

This research output has an Altmetric Attention Score of 1. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 16 December 2015.
All research outputs
#19,246,640
of 23,852,579 outputs
Outputs from arXiv
#558,679
of 990,619 outputs
Outputs of similar age
#241,886
of 329,385 outputs
Outputs of similar age from arXiv
#7,254
of 15,296 outputs
Altmetric has tracked 23,852,579 research outputs across all sources so far. This one is in the 11th percentile – i.e., 11% of other outputs scored the same or lower than it.
So far Altmetric has tracked 990,619 research outputs from this source. They receive a mean Attention Score of 4.0. This one is in the 29th percentile – i.e., 29% of its peers scored the same or lower than it.
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We're also able to compare this research output to 15,296 others from the same source and published within six weeks on either side of this one. This one is in the 33rd percentile – i.e., 33% of its contemporaries scored the same or lower than it.

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