A q-Dwork-type generalization of Rodriguez-Villegas’ supercongruences
نویسندگان
چکیده
Guo and Zudilin [Adv. Math. 346 (2019), 329–358] developed an analytical method, called “creative microscoping”, to prove many supercongruences by establishing their q-analogues. We apply this method give a q-Dwork-type generalization of Rodriguez-Villegas’ supercongruences, which was recently conjectured Zudilin.
منابع مشابه
Supercongruence Conjectures of Rodriguez-villegas
Abstract. In examining the relationship between the number of points over Fp on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified 22 possible supercongruences. We provide a framework of congruences covering all 22 cases. Using this framework we prove one of the outstanding supercongruence conjectures bet...
متن کاملOn a Supercongruence Conjecture of Rodriguez-villegas
In examining the relationship between the number of points over Fp on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified numerically 22 possible supercongruences. We prove one of the outstanding supercongruence conjectures between a special value of a truncated generalized hypergeometric series and the p-...
متن کاملa generalization of strong causality
در این رساله t_n - علیت قوی تعریف می شود. این رده ها در جدول علیت فضا- زمان بین علیت پایدار و علیت قوی قرار دارند. یک قضیه برای رده بندی آنها ثابت می شود و t_n- علیت قوی با رده های علی کارتر مقایسه می شود. همچنین ثابت می شود که علیت فشرده پایدار از t_n - علیت قوی نتیجه می شود. بعلاوه به بررسی رابطه نظریه دامنه ها با نسبیت عام می پردازیم و ثابت می کنیم که نوع خاصی از فضا- زمان های علی پایدار, ب...
COMPUTING WEIGHT 2 MODULAR FORMS OF LEVEL p 2 ARIEL PACETTI AND FERNANDO RODRIGUEZ VILLEGAS
For a prime p we describe an algorithm for computing the Brandt matrices giving the action of the Hecke operators on the space V of modular forms of weight 2 and level p2. For p ≡ 3 mod 4 we define a special Hecke stable subspace V0 of V which contains the space of modular forms with CM by the ring of integers of Q( √−p) and we describe the calculation of the corresponding Brandt matrices.
متن کاملRamanujan-type Supercongruences
We present several supercongruences that may be viewed as p-adic analogues of Ramanujan-type series for 1/π and 1/π 2 , and prove three of these examples.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2021
ISSN: ['0035-7596', '1945-3795']
DOI: https://doi.org/10.1216/rmj.2021.51.2179