Generalized Frobenius partitions

Generalized Frobenius partitions

by Andrews, George E.

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This paper is devoted to the study of equilength two-line arrays of non-negative integers. These are called generalized Frobenius partitions. It is shown that such objects have numerous interactions with modular forms, Kloosterman quadratic forms, the Lusztig-Macdonald-Wall conjectures as well as with classical theta functions and additive number theory.

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Title Statements

  • Full title :Generalized Frobenius partitions / George E. Andrews.

Summary

This paper is devoted to the study of equilength two-line arrays of non-negative integers. These are called generalized Frobenius partitions. It is shown that such objects have numerous interactions with modular forms, Kloosterman quadratic forms, the Lusztig-Macdonald-Wall conjectures as well as with classical theta functions and additive number theory.

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Edition Statements

  • Publication Date:©1984.

Publication Statements

Notes

"May 1984, volume 49, number 301 (third of 5 number)."

The Physical Object

  • Description:iv, 44 pages ; : 26 cm.

Edition Identifiers

  • ISBN:0821823027, 9780821823026
  • oclc:ocm10532967
  • LC Classification:QA3
  • Dewey Decimal:510 s

Table of Contents

Introduction -- Frobenius's idea -- The Jacobi triple product identity and the general principle -- Definitions and simple examples -- Generating functions -- Finite generating functions -- Hecke modular forms -- [italic]q-series -- Kloosterman quadratic forms -- Congruences -- The Dyson rank for [italic]F-partitions -- Partition identities -- Asymptotics -- F. Franklin's method -- Conclusion and open problems -- Tables.

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Subjects

Formes modulaires Forms, Modular Modulform Partitions (Mathematics) Partitions (Mathématiques) Problemas Combinatorios Classicos Quadratische Form Teoria dos numeros

Writers

Andrews, George E.

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