Some congruences with $q$−binomial sums

Neşe ÖMÜR, (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, Türkiye)
Zehra Betül GÜR, (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, Türkiye)
Sibel KOPARAL, (Bursa Uludağ Üniversitesi, Fen debiyat Fakültesi, Matematik Bölümü, Bursa, Türkiye)
Laid ELKHİRİ (Department of Mathematics, Laboratory of Recits, Tiaret University, Algiers, Algeria)
Turkish Journal of Mathematics
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Yıl: 2023 Cilt: 47 Sayı: 7 Sayfa Aralığı: 2006 - 2027 Metin Dili: İngilizce DOI: 10.55730/1300-0098.3478 İndeks Tarihi: 14-03-2024

Some congruences with $q$−binomial sums

Öz:
In this paper, using some combinatorial identities and congruences involving q− harmonic numbers, we establish congruences that for any odd prime p and any positive integer α , $sum_{k=1 (mod 2))}^{p-1} (-1)^{nk}tfrac{q^{-alpha npk+nbinom{k+1}{2}+2k }}{[k]_{q}}begin{bmatrix} alpha p-1 k end{bmatrix}_{q}^{n} quad (mod [p]_{q}^{2})$ $sum_{k=1 (mod 2))}^{p-1} (-1)^{nk}tfrac{q^{-alpha npk+nbinom{k+1}{2}+k }}{[k]_{q}}begin{bmatrix} alpha p-1 k end{bmatrix}_{q}^{n} tilde{H}_{k}(q) quad (mod [p]_{q}^{2})$ where n is any integer.
Anahtar Kelime: Congruence $q$−analog $q$−harmonic number

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA ömür n, Gür Z, koparal s, Elkhırı l (2023). Some congruences with $q$−binomial sums. , 2006 - 2027. 10.55730/1300-0098.3478
Chicago ömür neşe,Gür Zehra Betül,koparal sibel,Elkhırı laıd Some congruences with $q$−binomial sums. (2023): 2006 - 2027. 10.55730/1300-0098.3478
MLA ömür neşe,Gür Zehra Betül,koparal sibel,Elkhırı laıd Some congruences with $q$−binomial sums. , 2023, ss.2006 - 2027. 10.55730/1300-0098.3478
AMA ömür n,Gür Z,koparal s,Elkhırı l Some congruences with $q$−binomial sums. . 2023; 2006 - 2027. 10.55730/1300-0098.3478
Vancouver ömür n,Gür Z,koparal s,Elkhırı l Some congruences with $q$−binomial sums. . 2023; 2006 - 2027. 10.55730/1300-0098.3478
IEEE ömür n,Gür Z,koparal s,Elkhırı l "Some congruences with $q$−binomial sums." , ss.2006 - 2027, 2023. 10.55730/1300-0098.3478
ISNAD ömür, neşe vd. "Some congruences with $q$−binomial sums". (2023), 2006-2027. https://doi.org/10.55730/1300-0098.3478
APA ömür n, Gür Z, koparal s, Elkhırı l (2023). Some congruences with $q$−binomial sums. Turkish Journal of Mathematics, 47(7), 2006 - 2027. 10.55730/1300-0098.3478
Chicago ömür neşe,Gür Zehra Betül,koparal sibel,Elkhırı laıd Some congruences with $q$−binomial sums. Turkish Journal of Mathematics 47, no.7 (2023): 2006 - 2027. 10.55730/1300-0098.3478
MLA ömür neşe,Gür Zehra Betül,koparal sibel,Elkhırı laıd Some congruences with $q$−binomial sums. Turkish Journal of Mathematics, vol.47, no.7, 2023, ss.2006 - 2027. 10.55730/1300-0098.3478
AMA ömür n,Gür Z,koparal s,Elkhırı l Some congruences with $q$−binomial sums. Turkish Journal of Mathematics. 2023; 47(7): 2006 - 2027. 10.55730/1300-0098.3478
Vancouver ömür n,Gür Z,koparal s,Elkhırı l Some congruences with $q$−binomial sums. Turkish Journal of Mathematics. 2023; 47(7): 2006 - 2027. 10.55730/1300-0098.3478
IEEE ömür n,Gür Z,koparal s,Elkhırı l "Some congruences with $q$−binomial sums." Turkish Journal of Mathematics, 47, ss.2006 - 2027, 2023. 10.55730/1300-0098.3478
ISNAD ömür, neşe vd. "Some congruences with $q$−binomial sums". Turkish Journal of Mathematics 47/7 (2023), 2006-2027. https://doi.org/10.55730/1300-0098.3478
Sayfa Oluşturulma Tarihi
24-04-2024 9:48

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