title: Congruences modulo ρ between ρ-wisted Hasse-Weil L-values

authors: Delbourgo, Daniel

subjects: Science & Technology

abstract: Suppose E₁ and E₂ are semistable elliptic curves over Q with good reduction at p, whose associated weight two newforms f₁  and f₂ have congruent Fourier coefficients modulo p. Let RS(E*, ρ) denote the algebraic padic L-value attached to each elliptic curve E, twisted by an irreducible Artin representation, ρ, factoring through the Kummer extension Q(μp∞, Δ1/p∞).
If E₁ and E₂ have good ordinary reduction at p, we prove that RS(E₁, ρ) ≡ RS(E₂, ρ) mod p, under an integrality hypothesis for the modular symbols defined over the field cut out by Ker(ρ). Under this hypothesis, we establish that E₁ and E₂ have the same analytic λ-invariant at ρ.
Alternatively, if E₁ and E₂ have good supersingular reduction at p, we show that |RS(E₁, ρ) − RS(E₂, ρ)|ₚ < p ᵒʳᵈᵖ⁽ᶜᵒⁿᵈ⁽ρ⁾⁾/².
These congruences generalise some earlier work of Vatsal [Duke Math. J. 98 (1999), pp. 399–419], Shekhar–Sujatha [Trans. Amer. Math. Soc. 367 (2015), pp. 3579–3598], and Choi-Kim [Ramanujan J. 43 (2017), p. 163–195], to the false Tate curve setting.

text: Congruences modulo ρ between ρ-wisted Hasse-Weil L-values Suppose E₁ and E₂ are semistable elliptic curves over Q with good reduction at p, whose associated weight two newforms f₁  and f₂ have congruent Fourier coefficients modulo p. Let RS(E*, ρ) denote the algebraic padic L-value attached to each elliptic curve E, twisted by an irreducible Artin representation, ρ, factoring through the Kummer extension Q(μp∞, Δ1/p∞).
If E₁ and E₂ have good ordinary reduction at p, we prove that RS(E₁, ρ) ≡ RS(E₂, ρ) mod p, under an integrality hypothesis for the modular symbols defined over the field cut out by Ker(ρ). Under this hypothesis, we establish that E₁ and E₂ have the same analytic λ-invariant at ρ.
Alternatively, if E₁ and E₂ have good supersingular reduction at p, we show that |RS(E₁, ρ) − RS(E₂, ρ)|ₚ < p ᵒʳᵈᵖ⁽ᶜᵒⁿᵈ⁽ρ⁾⁾/².
These congruences generalise some earlier work of Vatsal [Duke Math. J. 98 (1999), pp. 399–419], Shekhar–Sujatha [Trans. Amer. Math. Soc. 367 (2015), pp. 3579–3598], and Choi-Kim [Ramanujan J. 43 (2017), p. 163–195], to the false Tate curve setting.

year: 2018

title: Biofuels and the poor: Global impact pathways of biofuels on agricultural markets

authors: Huang, Jikun

subjects: Biofuels

abstract: This study seeks to assess the future impacts of biofuel production on regional agricultural and related sectors over the next decade with a specific focus on the vulnerable regions of developing nations. Using a modification of the GTAP modeling platform to account for the global interactions of regional biofuel and food markets, the analysis shows that biofuel production levels depend on the assumption about the future price of energy and the nature of the substitutability between biofuels and petroleum-based transport fuels. Low energy prices reduce the demand for biofuels and thus require greater government support to meet the desired production targets. At the other extreme, when prices are high and there is scope for substituting biofuels for petroleum-based fuels, the volume of biofuels produced will exceed the mandates. Even when biofuels are being mainly produced in developed countries, our results indicate that there are impact pathways that extend far beyond the borders of the US, Brazil and the EU. Prices of feedstock and non-feedstock commodities rise in developing countries. There is also a rise in value added from the agricultural sector—a gain that is enjoyed by the owners of land and labor, including unskilled. Hence, to the extent that agriculture is a key sector in getting growth started and addressing poverty needs, the emergence of biofuels can (in this way at least) be a positive force.

text: Biofuels and the poor: Global impact pathways of biofuels on agricultural markets This study seeks to assess the future impacts of biofuel production on regional agricultural and related sectors over the next decade with a specific focus on the vulnerable regions of developing nations. Using a modification of the GTAP modeling platform to account for the global interactions of regional biofuel and food markets, the analysis shows that biofuel production levels depend on the assumption about the future price of energy and the nature of the substitutability between biofuels and petroleum-based transport fuels. Low energy prices reduce the demand for biofuels and thus require greater government support to meet the desired production targets. At the other extreme, when prices are high and there is scope for substituting biofuels for petroleum-based fuels, the volume of biofuels produced will exceed the mandates. Even when biofuels are being mainly produced in developed countries, our results indicate that there are impact pathways that extend far beyond the borders of the US, Brazil and the EU. Prices of feedstock and non-feedstock commodities rise in developing countries. There is also a rise in value added from the agricultural sector—a gain that is enjoyed by the owners of land and labor, including unskilled. Hence, to the extent that agriculture is a key sector in getting growth started and addressing poverty needs, the emergence of biofuels can (in this way at least) be a positive force.

year: 2012

title: Early French views of the Waikato and its inhabitants (1840-54)

authors: Jennings, William

abstract: This paper will investigate how the cultural background of these Frenchmen informed their descriptions of Waikato Maori and the Waikato environment. It will use the newly-published ten-volume collected correspondence of the pioneer Marists in the Pacific,the Lettres refues d'Odanie, as its principal source.

text: Early French views of the Waikato and its inhabitants (1840-54) This paper will investigate how the cultural background of these Frenchmen informed their descriptions of Waikato Maori and the Waikato environment. It will use the newly-published ten-volume collected correspondence of the pioneer Marists in the Pacific,the Lettres refues d'Odanie, as its principal source.

year: 2011