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Partition-theoretic Abelian theorems

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 نشر من قبل Robert Schneider
 تاريخ النشر 2020
  مجال البحث
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 تأليف Robert Schneider




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Using a theorem of Frobenius filtered through partition generating function techniques, we prove partition-theoretic and $q$-series Abelian theorems, yielding analogues of Abels convergence theorem for complex power series, and related formulas. As an application we give a limiting formula for the $q$-bracket of Bloch and Okounkov, an operator from statistical physics connected to the theory of modular forms, as $qto 1$ from within the unit disk.



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