Preprint (2005-05-25), arXiv:math.CO/0505548. ON q-EULER NUMBERS, q-SALIÉ NUMBERS AND q-CARLITZ NUMBERS

. CO / 0505548 . ON q - EULER NUMBERS AND q - SALIÉ NUMBERS

Acta Arith. 124(2006), no. 1, 41–57. ON q-EULER NUMBERS, q-SALIÉ NUMBERS AND q-CARLITZ NUMBERS

for any nonnegative integers n, s, t with 2 ∤ t, where [k]q = (1−q)/(1−q); this is a q-analogue of Stern’s congruence E2n+2s ≡ E2n +2 (mod 2s+1). We also prove that (−q; q)n = ∏ 0<k6n(1 + q ) divides S2n(q) and the numerator of C2n(q); this extends Carlitz’s result that 2 divides the Salié number S2n and the numerator of the Carlitz number C2n. Our result on q-Salié numbers implies a conjecture...

Arith . , in press . ON q - EULER NUMBERS , q - SALIÉ NUMBERS AND q -

for any nonnegative integers n, s, t with 2 ∤ t, where [k]q = (1−q)/(1−q); this is a q-analogue of Stern’s congruence E2n+2s ≡ E2n +2 (mod 2s+1). We also prove that (−q; q)n = ∏ 0<k6n(1 + q ) divides S2n(q) and the numerate of C2n(q); this extends Carlitz’s result that 2 divides the Salié number S2n and the numerate of the Carlitz number C2n. Our result on q-Salié numbers implies a conjecture o...

q-EULER AND GENOCCHI NUMBERS

Carlitz has introduced an interesting q-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the q-Euler numbers. In this paper we give another construction of q-Euler numbers, which are different than his q-Euler numbers. By using our q-Euler numbers, we define the q-analogue of Genocchi numbers ...

2 Hao Pan and Zhi

for any nonnegative integers n, s, t with 2 ∤ t, where [k]q = (1−q)/(1−q), this is a q-analogue of Stern’s congruence E2n+2s ≡ E2n +2 (mod 2s+1). We also prove that (−q; q)n = ∏ 0<k6n(1 + q ) divides S2n(q) and the numerate of C2n(q), this extends Carlitz’s result that 2 divides the Salié number S2n and the numerate of the Carlitz number C2n. For q-Salié numbers we also confirm a conjecture of ...