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padic modular forms over Shimura curves over Q. Thesis
, 1999
"... Abstract. We set up the basic theory of Padic modular forms over certain unitary PEL Shimura curves M ′K ′. For any PEL abelian scheme classified by M K ′ , which is not “too supersingular”, we construct a canonical subgroup which is essentially a lifting of the kernel of Frobenius from characteris ..."
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Cited by 17 (5 self)
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function of the weight. Introduction. The theory of padic modular forms started with the work of J.P. Serre, B. Dwork and N. Katz. The original motivation for this theory was the problem of padic interpolation of special values of the Riemann zeta function. Serre [16] defined padic modular forms as padic
A generalization of Sturmian sequences; combinatorial structure and transcendence
 Acta Arith
"... In this paper we study dynamical properties of a class of uniformly recurrent sequences on a kletter alphabet with complexity p(n) = (k − 1)n + 1. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of the (binary) Sturmian sequences of Morse and Hedlund. We ..."
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Cited by 40 (8 self)
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of the form V 2+ɛ and in the Sturmian case arbitrarily large subwords of the form V 3+ɛ. Combined with a recent combinatorial version of Ridout’s Theorem due to S. Ferenczi and C. Mauduit, we prove that an irrational number whose base bdigit expansion is an ArnouxRauzy sequence, is transcendental
FPGA Implementation of Point Multiplication on Koblitz Curves using Kleinian Integers
 In Cryptographic Hardware and Embedded Systems, CHES 2006
, 2006
"... Abstract. We describe algorithms for point multiplication on Koblitz curves using multiplebase expansions of the form k = ∑ ±τ a (τ − 1) b and k = ∑ ±τ a (τ − 1) b (τ 2 − τ − 1) c. We prove that the number of terms in the second type is sublinear in the bit length of k, which leads to the first p ..."
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Cited by 15 (6 self)
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Abstract. We describe algorithms for point multiplication on Koblitz curves using multiplebase expansions of the form k = ∑ ±τ a (τ − 1) b and k = ∑ ±τ a (τ − 1) b (τ 2 − τ − 1) c. We prove that the number of terms in the second type is sublinear in the bit length of k, which leads to the first
THE CLASS NUMBER OF Q ( √ −p) AND DIGITS OF 1/p
"... Abstract. Let p be a prime number such that p ≡ 1(modr) for some integer r>1. Let g>1 be an integer such that g has order r in (Z/pZ) ∗.Let 1 p = ∞ ∑ xk g k=1 k be the gadic expansion. Our result implies that the “average ” digit in the gadic expansion of 1/p is (g − 1)/2 with error term in ..."
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Abstract. Let p be a prime number such that p ≡ 1(modr) for some integer r>1. Let g>1 be an integer such that g has order r in (Z/pZ) ∗.Let 1 p = ∞ ∑ xk g k=1 k be the gadic expansion. Our result implies that the “average ” digit in the gadic expansion of 1/p is (g − 1)/2 with error term
ACTA ARITHMETICA LXVII.2 (1994)
"... On special values of generalized padic hypergeometric functions by Kaori Ota (Tokyo) We generalize results for ratios of generalized hypergeometric functions obtained by P. T. Young [9] to the case of a power of p. More precisely, we generalize Theorems 3.2 and 3.4 in [9]. In order to do that, intr ..."
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this paper, p is a prime, νp denotes the padic valuation normalized by νp(p) = 1 and by the padic expansion we mean the standard padic expansion whose coefficients are all in {0, 1,..., p − 1}. 1. The padic Gamma function is defined by Γp(n+ 1) = (−1)n+1 n∏ j=1 p j j for a positive integer n
Exploring slopes of padic modular forms
, 2000
"... Let p be prime, N be a positive integer prime to p, and k be an integer. Let Pk(t) be the characteristic series for Atkin’s U operator as an endomorphism of padic overconvergent modular forms of tame level N and weight k. Motivated by conjectures of Gouvêa and Mazur, we strengthen a congruence in [ ..."
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Cited by 8 (0 self)
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relatively prime to p, and k be an integer. Let B be a padic ring between Zp and Øp, the ring of integers in Cp. Denote by Mk(N,B) the padic overconvergent modular forms of tame level N and weight k and by Sk(N,B) the subspace of overconvergent cusp forms. For every weight k, Atkin’s U operator
CONTINUED FRACTIONS OF GIVEN SYMMETRIC PERIOD F r a n z
, 1989
"... 1. If D> 1 is a rational number, not a square, then has a (simple) continued fraction expansion of the form fD = [b0, b19..., bk_l9 2b0] with &> 1 and positive integers b ± such that the sequence {b\9...5 £&].) is symmetric, i.e., 2 ^ = Zty ^ for all i e {1,..., k 1}. Necessary and ..."
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1. If D> 1 is a rational number, not a square, then has a (simple) continued fraction expansion of the form fD = [b0, b19..., bk_l9 2b0] with &> 1 and positive integers b ± such that the sequence {b\9...5 £&].) is symmetric, i.e., 2 ^ = Zty ^ for all i e {1,..., k 1}. Necessary
padic Banach modules of arithmetical modular forms and triple products of Coleman's families
, 2006
"... For a prime number p ≥ 5, we consider three classical cusp eigenforms fj(z) = an,je(nz) ∈ Skj (Nj, ψj), (j = 1, 2, 3) n=1 of weights k1, k2, k3, of conductors N1, N2, N3, and of nebentypus characters ψj mod Nj. According to H.Hida [Hi86] and R.Coleman [CoPB], one can include each fj (j = 1, 2, 3) ..."
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) (under suitable assumptions on p and on fj) into a padic analytic family kj ↦ → {fj,kj = an(fj,kj)qn} n=1 of cusp eigenforms fj,kj of weights kj in such a way that fj,kj = fj, and that all their Fourier coe cients an(fj,kj) are given by certain padic analytic functions kj ↦ → an,j(kj). The purpose
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"... n≥1 anqn be a normalized Hecke eigenform of level Np, where N ≥ 1 is an integer and p ∤ N a prime number, which is pnew. The main result of this paper is an equality L GS (f) = L D (ϕ ± g) between two padic Linvariants attached to f: one is the GreenbergStevens Linvariant LGS (f), and the othe ..."
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in a suitable padic disk U ⊆ Zp × Z/(p − 1)Z containing 2, and f(k) = an(f, k)q n n=1 is the qexpansion of the Hida family passing through f (so f(2) = f). The second Linvariant, LD (ϕ ± g), is attached to the JacquetLanglands lift g of f to a Shimura curve C associated with a quaternion algebra
Results 11  20
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