-analogue of a binomial coefficient congruence.
-analogue of the Lucas congruence. (Zum -Analogon der Kongruenz von Lucas.)
-analogues of the Hermite polynomials. (Les -analogues des polynômes d'Hermite.)
-analogues of the sums of consecutive integers, squares, cubes, quarts and quints.
-analogues of two supercongruences of Z.-W. Sun
We give several different -analogues of the following two congruences of Z.-W. Sun: where is an odd prime, is a positive integer, and is the Jacobi symbol. The proofs of them require the use of some curious -series identities, two of which are related to Franklin’s involution on partitions into distinct parts. We also confirm a conjecture of the latter author and Zeng in 2012.
-Bernoulli numbers associated with -Stirling numbers.
-binomials and the greatest common divisor.
-counting descent pairs with prescribed tops and bottoms.
-Eulerian polynomials and polynomials with only real zeros.
-exponential families.
-extensions for the Apostol–Genocchi polynomials.
-Genocchi numbers and polynomials associated with -Genocchi-type -functions.
-identities related to overpartitions and divisor functions.
-Riemann zeta function.
-Selberg integrals and Macdonald polynomials
q-difference equations and Ramanujan-Selberg continued fractions
q-Identities for Maass waveforms.
Qseries Maple tutorial: A -product tutorial for a -series Maple package.
Quadratic Equations over Finite Fields and Class Numbers of Real Quadratic Fields.
Quasi-particle fermionic formulas for (k, 3)-admissible configurations
We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.