Explorations in the Theory of Partition Zeta Functions

DOI10.1007/978-3-319-59969-4_10zbMath1497.11234arXiv1605.05536OpenAlexW2405879972MaRDI QIDQ5038231

Larry Rolen, Ken Ono, Robert P. Schneider

Publication date: 30 September 2022

Published in: Exploring the Riemann Zeta Function (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.05536

zbMATH Keywords

multiple zeta valuespartition zeta functions

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Other Dirichlet series and zeta functions (11M41) Holomorphic modular forms of integral weight (11F11) Analytic theory of partitions (11P82) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items

A ``supernormal partition statistic ⋮ Sequentially congruent partitions and related bijections ⋮ A formula for the number of partitions of \(n\) in terms of the partial Bell polynomials ⋮ Analysis and combinatorics of partition zeta functions

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Partition zeta functions
• Multiplicative partitions
• A combinatorial identity of multiple zeta values with even arguments
• Evaluation of the multiple zeta values \(\zeta(2,\ldots,2,3,2,\ldots,2)\)
• Zeta-polynomials for modular form periods
• On gamma quotients and infinite products
• Periods of modular forms and Jacobi theta functions
• Multiple harmonic series
• On an additive arithmetic function
• Evaluations of \(k\)-fold Euler/Zagier sums: a compendium of results for arbitrary \(k\)
• Product partitions and recursion formulae
• Motives for modular forms
• \(p\)-adic multiple zeta values. I: \(p\)-adic multiple polylogarithms and the \(p\)-adic KZ equation
• On the polynomials with all their zeros on the unit circle
• The character of the infinite wedge representation
• Notes on the roots of Ehrhart polynomials
• Periods of modular forms on \(\Gamma_0(N)\) and products of Jacobi theta functions
• Lattice polytopes, Hecke operators, and the Ehrhart polynomial
• Norm bounds for Ehrhart polynomial roots
• Local zeta factors and geometries under SpecZ
• Modular forms and period polynomials
• The Nontrivial Zeros of Period Polynomials of Modular Forms Lie on the Unit Circle
• Riemann hypothesis for period polynomials of modular forms
• On the parity of the number of multiplicative partitions
• On the zeros of certain polynomials
• Combinatorial relations for Euler–Zagier sums
• The arithmetic of the values of modular functions and the divisors of modular forms
• Unimodularity of zeros of period polynomials of Hecke eigenforms
• Derivation and double shuffle relations for multiple zeta values
• Concerning Two Series for the Gamma Function
• Congruences of modular forms and Selmer groups