AbstractIn 1992, Strauss, Shallit and Zagier proved that for any positive integer a,∑k=03a−1(2kk)≡0(mod32a) and furthermore132a∑k=03a−1(2kk)≡1(mod3). Recently a q-analogue of the first congruence was conjectured by Guo and Zeng. In this paper we prove the conjecture of Guo and Zeng, and also give a q-analogue of the second congruence
AbstractThe ψ-operator for (ϕ,Γ)-modules plays an important role in the study of Iwasawa theory via ...
AbstractLet p≡1(mod4) be a prime and a,b∈Z with a2+b2≠p. Suppose p=x2+(a2+b2)y2 for some integers x ...
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractWe present some variations on the Greene–Krammerʼs identity which involve q-Catalan numbers....
AbstractLet q>1 and m>0 be relatively prime integers. We find an explicit period νm(q) such that for...
AbstractLet a and b be positive integers and let p be an odd prime such that p=ax2+by2 for some inte...
AbstractLet p≡1(mod4) be a prime. Let a,b∈Z with p∤a(a2+b2). In the paper we mainly determine (b+a2+...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
AbstractRecently, R. Tauraso established finite p-analogues of Apéryʼs famous series for ζ(2) and ζ(...
The purpose of this paper is to investigate some properties of q-Euler numbers and polynomials with ...
AbstractLet {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(...
AbstractIn this paper, we prove a new identity for the product of two partial theta functions. An im...
AbstractWe introduce multiple q-Mahler measures and we calculate some specific examples, where multi...
AbstractIn this paper we establish a q-analogue of a congruence of Sun concerning the products of bi...
AbstractThe ψ-operator for (ϕ,Γ)-modules plays an important role in the study of Iwasawa theory via ...
AbstractLet p≡1(mod4) be a prime and a,b∈Z with a2+b2≠p. Suppose p=x2+(a2+b2)y2 for some integers x ...
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractWe present some variations on the Greene–Krammerʼs identity which involve q-Catalan numbers....
AbstractLet q>1 and m>0 be relatively prime integers. We find an explicit period νm(q) such that for...
AbstractLet a and b be positive integers and let p be an odd prime such that p=ax2+by2 for some inte...
AbstractLet p≡1(mod4) be a prime. Let a,b∈Z with p∤a(a2+b2). In the paper we mainly determine (b+a2+...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
AbstractRecently, R. Tauraso established finite p-analogues of Apéryʼs famous series for ζ(2) and ζ(...
The purpose of this paper is to investigate some properties of q-Euler numbers and polynomials with ...
AbstractLet {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for Bj(...
AbstractIn this paper, we prove a new identity for the product of two partial theta functions. An im...
AbstractWe introduce multiple q-Mahler measures and we calculate some specific examples, where multi...
AbstractIn this paper we establish a q-analogue of a congruence of Sun concerning the products of bi...
AbstractThe ψ-operator for (ϕ,Γ)-modules plays an important role in the study of Iwasawa theory via ...
AbstractLet p≡1(mod4) be a prime and a,b∈Z with a2+b2≠p. Suppose p=x2+(a2+b2)y2 for some integers x ...
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
DOI
Add to ORKG