q-Analogues of some supercongruences related to Euler numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

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EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s147474802100027x ◽

2021 ◽

pp. 1-66

Author(s):

Tom Bachmann ◽

Kirsten Wickelgren

Keyword(s):

Commutative Algebra ◽

Vector Bundles ◽

Euler Class ◽

Complete Intersections ◽

Bilinear Forms ◽

Euler Numbers ◽

Coherent Sheaves ◽

Linear Subspaces ◽

Algebraic Vector

Abstract We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class and give formulas for local indices at isolated zeros, both in terms of the six-functors formalism of coherent sheaves and as an explicit recipe in the commutative algebra of Scheja and Storch. As an application, we compute the Euler classes enriched in bilinear forms associated to arithmetic counts of d-planes on complete intersections in $\mathbb P^n$ in terms of topological Euler numbers over $\mathbb {R}$ and $\mathbb {C}$ .

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Some arithmetic properties of the q-Euler numbers and q-Salié numbers

European Journal of Combinatorics ◽

10.1016/j.ejc.2005.04.009 ◽

2006 ◽

Vol 27 (6) ◽

pp. 884-895 ◽

Cited By ~ 20

Author(s):

Victor J.W. Guo ◽

Jiang Zeng

Keyword(s):

Euler Numbers ◽

Arithmetic Properties

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Some Identities Involving the Fubini Polynomials and Euler Polynomials

Mathematics ◽

10.3390/math6120300 ◽

2018 ◽

Vol 6 (12) ◽

pp. 300 ◽

Cited By ~ 4

Author(s):

Guohui Chen ◽

Li Chen

Keyword(s):

Power Series ◽

Second Order ◽

Euler Polynomials ◽

Euler Numbers ◽

Non Linear ◽

Combinatorial Methods

In this paper, we first introduce a new second-order non-linear recursive polynomials U h , i ( x ) , and then use these recursive polynomials, the properties of the power series and the combinatorial methods to prove some identities involving the Fubini polynomials, Euler polynomials and Euler numbers.

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Some Symmetric Identities Involving Fubini Polynomials and Euler Numbers

Symmetry ◽

10.3390/sym10080303 ◽

2018 ◽

Vol 10 (8) ◽

pp. 303 ◽

Cited By ~ 8

Author(s):

Zhao Jianhong ◽

Chen Zhuoyu

Keyword(s):

Calculation Method ◽

Computational Formula ◽

Euler Numbers ◽

Special Sequence ◽

Computational Problem ◽

Elementary Methods ◽

Symmetric Identities ◽

Recursive Calculation

The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.

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