Browsing by Subject "Congruences"

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The Congruence Properties of Romik’s Sequence of Taylor Coefficients of Jacobi’s Theta Function $θ_3$

[OWP-2024-12] Krattenthaler, Christian; Müller, Thomas W. (Mathematisches Forschungsinstitut Oberwolfach, 2024-11-29)

In [Ramanujan J. 52 (2020), 275-290], Romik considered the Taylor expansion of Jacobi's theta function $\theta_3(q)$ at $q=e^{-\pi}$ and encoded it in an integer sequence $(d(n))_{n\ge0}$ for which he provided a recursive ...
Congruences Associated with Families of Nilpotent Subgroups and a Theorem of Hirsch

[OWP-2019-16] Aivazidis, Stefanos; Müller, Thomas (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-27)

Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number ...