Algebraic and transcendental formulas for the smallest parts function

DOI10.1016/j.aim.2015.11.011zbMath1407.11058arXiv1504.02500OpenAlexW1642346117MaRDI QIDQ904023

Nickolas Andersen, Scott Ahlgren

Publication date: 15 January 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.02500

zbMATH Keywords

theta liftsmallest parts functionharmonic Maass formssums of Kloosterman sums

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Theta series; Weil representation; theta correspondences (11F27) Gauss and Kloosterman sums; generalizations (11L05) Elementary theory of partitions (11P81)

Related Items (17)

Inequalities for the overpartition function ⋮ Effective estimates for the smallest parts function ⋮ Theta lifts for Lorentzian lattices and coefficients of mock theta functions ⋮ THE ASYMPTOTIC DISTRIBUTION OF TRACES OF WEAK MAASS FORMS ⋮ The asymptotic distribution of Andrews' smallest parts function ⋮ Effective bounds for traces of weak Maass forms ⋮ On sums of Kloosterman and Gauss sums ⋮ Congruences for a mock modular form on \(\mathrm{SL}_2(\mathbb{Z})\) and the smallest parts function ⋮ Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products ⋮ On the non-negativity of the spt-crank for partitions without repeated odd parts ⋮ Bounds for coefficients of the \(f(q)\) mock theta function and applications to partition ranks ⋮ A polyharmonic Maass form of depth 3/2 for \(\mathrm{SL}_2(\mathbb{Z})\) ⋮ Effective bounds for the Andrews spt-function ⋮ Uniform bounds for sums of Kloosterman sums of half integral weight ⋮ An effective bound for the partition function ⋮ Hybrid subconvexity and the partition function ⋮ Locally harmonic Maass forms and periods of meromorphic modular forms

Uses Software

• DLMF

Cites Work

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• \(\ell \)-adic properties of smallest parts functions
• A sum connected with the series for the partition function
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
• On the explicit construction of higher deformations of partition statistics
• Borcherds products on \(O(2,l)\) and Chern classes of Heegner divisors
• Singular invariants and coefficients of harmonic weak Maass forms of weight \(5/2\)
• On two geometric theta lifts
• Sums of Kloosterman sums
• Combinatorial interpretations of congruences for the spt-function
• Twisted traces of CM values of weak Maass forms
• Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
• The \(f(q)\) mock theta function conjecture and partition ranks
• Formulas for the coefficients of half-integral weight harmonic Maaß forms
• Hecke operators on \(\Gamma_0(m)\)
• On the expansion of the partition functions in a series
• A derivation of the Hardy-Ramanujan formula from an arithmetic formula
• Congruences for Andrews’ spt-function modulo powers of $5$, $7$ and $13$
• Elliptic Modular Forms and Their Applications
• Hilbert Modular Forms and Their Applications
• Mock modular grids and Hecke relations for mock modular forms
• The number of smallest parts in the partitions of n
• CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK
• Modular forms of varying weights.
• A generalization of the Goldfeld-Sarnak estimate on Selberg's Kloosterman zeta-function
• Kloosterman Sums and Maass Cusp Forms of Half Integral Weight for the Modular Group
• Congruences for the Andrews spt function
• An arithmetic formula for the partition function
• HECKE-TYPE CONGRUENCES FOR ANDREWS' SPT-FUNCTION MODULO 16 AND 32
• Numerical computations with the trace formula and the Selberg eigenvalue conjecture
• Duality involving the mock theta function f (q )
• Traces of CM values of modular functions
• On Some Exponential Sums
• Some Asymptotic Formulae for the Mock Theta Series of Ramanujan
• Revisiting Rademacher's formula for the partition function \(p(n)\)

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