-analogue of a binomial coefficient congruence.
-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.
-Bernstein polynomials associated with -Stirling numbers and Carlitz's -Bernoulli numbers.
-binomials and the greatest common divisor.
-extensions for the Apostol–Genocchi polynomials.
-Genocchi numbers and polynomials associated with fermionic -adic invariant integrals on .
-Genocchi numbers and polynomials associated with -Genocchi-type -functions.
-identities related to overpartitions and divisor functions.
-Riemann zeta function.
-series, elliptic curves, and odd values of the partition function.
Q-curves over quadratic fields.
q-difference equations and Ramanujan-Selberg continued fractions
q-Identities for Maass waveforms.
q-Identities for Maass waveforms (Corrigendum).
Qseries Maple tutorial: A -product tutorial for a -series Maple package.
q-Stern Polynomials as Numerators of Continued Fractions
We present a q-analogue for the fact that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. Moreover, we give a combinatorial interpretation for our q-analogue.
Q(T)-rank of elliptic curves and certain limit coming from the local points.
Quadratic congruences on average and rational points on cubic surfaces
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A₅ + A₁.
Quadratic Differentials and Equivariant Deformation Theory of Curves
Given a finite -group acting on a smooth projective curve over an algebraically closed field of characteristic , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of acting on the space of global holomorphic quadratic differentials on . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when is cyclic or when the action of on is weakly...