On q -congruences related to Hn(x;q) and Mn(x;q)

Koparal S., ÖMÜR N., Elkhiri L.

Indian Journal of Pure and Applied Mathematics, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s13226-023-00520-0
  • Dergi Adı: Indian Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Anahtar Kelimeler: Congruence, Harmonic number, q-analog number
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this paper, we examine ∑k=mp-1qk[km]qHk(x;q)(mod[p]q) and Mp-1(x;q)(mod[p]q), where for real number x, Hn(x;q)=∑k=1nxk[k]q and Mn(x;q)=∑k=1nkxk[k]q. For example, for an odd prime number p and m∈ { 0 , 1 ,.. , p- 2 } , [m+1]q∑k=mp-1qk[km]qHk(x;q)≡(-1)mq-(m2)(1-(x;q)p)-qm(xq;q)mxm+1[p]x(mod[p]q).