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ARITHMETIC LAPLACIANS
, 2008
"... We develop an arithmetic analogue of elliptic partial differential equations. The rôle of the space coordinates is played by a family of primes, and that of the space derivatives along the various primes are played by corresponding Fermat quotient operators subjected to certain commutation relation ..."
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We develop an arithmetic analogue of elliptic partial differential equations. The rôle of the space coordinates is played by a family of primes, and that of the space derivatives along the various primes are played by corresponding Fermat quotient operators subjected to certain commutation
BINARY ARITHMETIC
"... In reference (1) algorithms for performing arithmetic with unsigned two's complement operands were described. The scheme for division was implemented in a set of multipleprecision floatingpoint arithmetic routines (2). User experience with those routines showed that there is one case where th ..."
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In reference (1) algorithms for performing arithmetic with unsigned two's complement operands were described. The scheme for division was implemented in a set of multipleprecision floatingpoint arithmetic routines (2). User experience with those routines showed that there is one case where
Arithmetic Varieties
, 2002
"... The ShimuraTaniyama conjecture states that the Mellin transform of the HasseWeil Lfunction of any elliptic curve defined over the rational numbers is a modular form. Recent work of Wiles, TaylorWiles and BreuilConradDiamondTaylor has provided a proof of this longstanding conjecture. Elliptic ..."
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curves provide the simplest framework for a class of CalabiYau manifolds which have been conjectured to be exactly solvable. It is shown that the HasseWeil modular form determined by the arithmetic structure of the Fermat type elliptic curve is related in a natural way to a modular form arising from
Cohomology of arithmetic families of (φ,Γ)modules
"... We prove the finiteness and compatibility with base change of the (ϕ,Γ)cohomology and the Iwasawa cohomology of arithmetic families of (ϕ,Γ)modules. Using this finiteness theorem, we show that a family of Galois representations that is densely pointwise refined in the sense of Mazur is actually t ..."
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Cited by 15 (5 self)
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We prove the finiteness and compatibility with base change of the (ϕ,Γ)cohomology and the Iwasawa cohomology of arithmetic families of (ϕ,Γ)modules. Using this finiteness theorem, we show that a family of Galois representations that is densely pointwise refined in the sense of Mazur is actually
ARITHMETIC OF CURVES
, 2011
"... In this course, we start with very basics of curves and try to reach the theory of their jacobians and at the end, we introduce modular Galois representation a la Eichler–Shimura: (1) Plane curves over a field (elementary, up to Section 3); (2) Scheme/group functor over a ring (a trytobe easy intr ..."
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In this course, we start with very basics of curves and try to reach the theory of their jacobians and at the end, we introduce modular Galois representation a la Eichler–Shimura: (1) Plane curves over a field (elementary, up to Section 3); (2) Scheme/group functor over a ring (a trytobe easy introduction to scheme theory); (3) Picard schemes and Jacobian of curves (more sophisticated hereafter); (4) General theory of abelian varieties; (5) Construction of modular Galois representation. Elliptic curves and modular curves are one of the most important objects studied in number theory. As everybody knows, the theory is a base of the proof by Wiles (through Ribet’s work) of Fermat’s last theorem, is the main tool in the proof of Serre’s mod p modularity conjecture (by Khare– Wintenberger), it supplies us with the simplest (and perhaps the most beautiful) example of Shimura varieties (cf. [IAT] Chapters 6 and 7), it supplies a fast prime factorization algorithm (cf. [REC] IV), and so on. Since this is a topic course, we give details of proofs in the first few weeks and later we try to introduce more uptodate materials in a less strict manner though in this notes, detailed
Arithmetic into Maple
, 2010
"... This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. ..."
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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which
Results 11  20
of
86,280