CrossRef
Open Access
2022
2 sitasi
NEW GENERALISATIONS OF VAN HAMME’S (G.2) SUPERCONGRUENCE
NA TANG
Abstrak
AbstractSwisher [‘On the supercongruence conjectures of van Hamme’, Res. Math. Sci.2 (2015), Article no. 18] and He [‘Supercongruences on truncated hypergeometric series’, Results Math.72 (2017), 303–317] independently proved that Van Hamme’s (G.2) supercongruence holds modulo $p^4$ for any prime $p\equiv 1\pmod {4}$ . Swisher also obtained an extension of Van Hamme’s (G.2) supercongruence for $p\equiv 3 \pmod 4$ and $p>3$ . In this note, we give new one-parameter generalisations of Van Hamme’s (G.2) supercongruence modulo $p^3$ for any odd prime p. Our proof uses the method of ‘creative microscoping’ introduced by Guo and Zudilin [‘A q-microscope for supercongruences’, Adv. Math.346 (2019), 329–358].
Penulis (1)
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NA TANG
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2022
- Bahasa
- en
- Total Sitasi
- 2×
- Sumber Database
- CrossRef
- DOI
- 10.1017/s000497272200048x
- Akses
- Open Access ✓