Twisted Klein curves modulo 2
نویسنده
چکیده
The equation goes back to F. Klein who derived it as a model for the modular curve X(7) [9]. In characteristic zero, the curve is the unique curve of genus three, up to isomorphism, with the maximal number of 168 automorphisms. Various aspects of the curve are described in the recent papers [8], [14], [6], in [7], and in other contributions to [10]. For further and older references dealing with the many fascinating combinatorial and arithmetic properties of the curve, we refer to these publications.
منابع مشابه
CRITICAL L - VALUES OF LEVEL p NEWFORMS ( mod p )
Suppose that p ≥ 5 is prime, that F(z) ∈ S2k(Γ0(p)) is a newform, that v is a prime above p in the field generated by the coefficients of F , and that D is a fundamental discriminant. We prove non-vanishing theorems modulo v for the twisted central critical values L(F⊗χD, k). For example, we show that if k is odd and not too large compared to p, then infinitely many of these twisted L-values ar...
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We prove that logarithmic derivatives of certain twisted Hilbert class polynomials are holomorphic modular forms modulo p of filtration p+1. We derive p-adic information about twisted Hecke traces and Hilbert class polynomials. In this framework we formulate a precise criterion for p-divisibility of class numbers of imaginary quadratic fields in terms of the existence of certain cusp forms modu...
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We show that twisted monomial Gauss sums modulo prime powers can be evaluated explicitly once the power is sufficiently large.
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It is a classical observation of Serre that the Hecke algebra acts locally nilpotently on the graded ring of modular forms modulo 2 for the full modular group. Here we consider the problem of classifying spaces of modular forms for which this phenomenon continues to hold. We give a number of consequences of this investigation as they relate to quadratic forms, partition functions, and central v...
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Let q be a large prime and χ the quadratic character modulo q. Let φ be a self-dual cuspidal Hecke eigenform for SL(3,Z), and f a Hecke-Maaß cusp form for Γ0(q) ⊆ SL2(Z). We consider the twisted L-functions L(s, φ × f × χ) and L(s, φ × χ) on GL(3) × GL(2) and GL(3) with conductors q6 and q3, respectively. We prove the subconvexity bounds L(1/2, φ× f × χ) φ,f,ε q, L(1/2 + it, φ× χ) φ,t,ε q for a...
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