p-Adic Properties of Coefficients of Weakly Holomorphic Modular Forms
نویسندگان
چکیده
منابع مشابه
p-ADIC PROPERTIES OF COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS
We examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and 5.
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is a weakly holomorphic modular form of integral or half-integral weight w2 on the congruence subgroup Γ1(N). By a weakly holomorphic modular form we mean a function f(z) which is holomorphic on the upper half-plane, meromorphic at the cusps, and which transforms in the usual way under the action of Γ1(N) on the upper half-plane (see, for example, [13] for generalities on modular forms of half-...
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A well known result is that if E2k is the Eisenstein series of weight 2k and 2k = 2k′ (mod (p− 1)p), then E2k = E2k′ (mod p). In words, this result tells us that the Eisenstein series form a natural family of modular forms that are p-adically interpolated in the weight aspect. Motivated by a question of Serre, we construct a second natural family of modular forms that have this same property. B...
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We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan τ -function, and use this to prove that these Fourier coefficients are often highly divisible by 2.
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2010
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnp240