Let f be a newform of weight 2k − 2 and level 1. In this paper we provide evidence for the Bloch-Kato conjecture for modular forms. We demonstrate an implication that under suitable hypotheses ifwhere p is a suitably chosen prime and a uniformizer of a finite extension K/Q p . We demonstrate this by establishing a congruence between the Saito-Kurokawa lift F f of f and a cuspidal Siegel eigenform G that is not a Saito-Kurokawa lift. We then examine what this congruence says in terms of Galois representations to produce a non-trivial p-torsion element in
Abstract. Let k > 3 be an integer and p a prime with p > 2k − 2. Let f be a newform of weight 2k − 2 and level 1 so that f is ordinary at p and ρ f is irreducible. Under some additional hypotheses we prove that ordp(L alg (k, f )) ≤ ordp(#S) where S is the Pontryagin dual of the Selmer group associated to ρ f ⊗ ε 1−k with ε the p-adic cyclotomic character. We accomplish this by first constructing a congruence between the Saito-Kurokawa lift of f and a non-CAP Siegel cusp form. Once this congruence is established, we use Galois representations to obtain the lower bound on the Selmer group.
Abstract. Let κ ≥ 6 be an even integer, M an odd square-free integer, and f ∈ S2κ−2(Γ0(M )) a newform. We prove that under some reasonable assumptions that half of the λ-part of the Bloch-Kato conjecture for the near central critical value L(κ, f ) is true. We do this by bounding the ℓ-valuation of the order of the appropriate Bloch-Kato Selmer group below by the ℓ-valuation of algebraic part of L(κ, f ). We prove this by constructing a congruence between the Saito-Kurokawa lift of f and a cuspidal Siegel modular form.
This study of hotels representing thirty-seven brands from fifty-six countries uncovers the market conditions under which investing resources in specific market strategies leads to higher performance. Specifically, the authors identified, for the first time in an international context, the circumstances under which customer orientation (acquisition, satisfaction, and retention of customers) alone has a higher payoff or when simply investing resources on competitor orientation (monitoring, managing, and outflanking competitors) alone is the better strategy. An additional interesting twist, not shown before to the authors' knowledge, is that in the cases where a customer-based strategy has a higher payoff, focusing on competitors diminishes performance. Similarly, in a market where competitor-based strategy has a higher payoff, a customer focus lowers performance.
Let f ∈ S2κ−2(Γ0(M)) be a Hecke eigenform with κ ≥ 2 even and M ≥ 1 and odd and square-free. In this paper we survey the construction of the Saito-Kurokawa lifting from the classical and representation theoretic point of view. We also provide some arithmetic results on the Fourier coefficients of Saito-Kurokawa liftings. We then calculate the norm of the Saito-Kurokawa lift.
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