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UID:node-3060816@mathematics.huji.ac.il
DTSTAMP:20211108T123000Z
DTSTART:20211108T123000Z
DTEND:20211108T140000Z
SUMMARY:HUJI NT Seminar - Arvind Kumar
DESCRIPTION:\n\nTitle: Ramanujan-style congruences for prime level.\n\nAbstract: The prototype of a Ramanujan congruence goes back to Ramanujan (1916) which asserts that the Ramanujan delta function is congruent to the Eisenstein series of weight 12 modulo 691. There are several well-known ways to prove, interpret, and generalize Ramanujan's congruence. For higher weights eigenforms of level 1, Ramanujan-style congruences have been obtained by Datskovsky-Guerzhoy whereas for newforms of prime level by Billerey-Menares and Dummigan-Fretwell. Recently, using the theory of period polynomials, Gaba-Popa (under some technical assumptions) extended these results by determining also the Atkin-Lehner eigenvalue of the newform involved. \n\nIn this talk, we refine the result of Gaba-Popa under a mild assumption by using completely different ideas. More precisely, we establish congruences modulo certain primes between a cuspidal newform and an Eisenstein series of weight k and prime level.
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