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33,041
Arithmetic of . . . AND RATIONAL CONFORMAL FIELD THEORY
, 2001
"... It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of CalabiYau manifolds and the underlying conformal field theory. Specifically it is pointed out how the algebraic number field ..."
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Cited by 3 (3 self)
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field determined by the fusion rules of the conformal field theory can be derived from the number theoretic structure of the cohomological HasseWeil Lfunction determined by Artin’s congruent zeta function of the algebraic variety. In this context a natural number theoretic characterization arises
Arithmetic Varieties from CalabiYau Arithmetic
, 2002
"... This paper describes a framework in which techniques from arithmetic algebraic geometry are used to formulate a direct and intrinsic link between the geometry of CalabiYau manifolds and aspects of the underlying conformal field theory. As an application the algebraic number field determined by the ..."
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by the fusion rules of the conformal field theory is derived from the number theoretic structure of the cohomological HasseWeil Lfunction determined by Artin’s congruent zeta function of the algebraic variety. In this context a natural number theoretic characterization arises for the quantum dimensions
Congruences for critical values of higher derivatives of twisted HasseWeil Lfunctions
, 2013
"... Let A be an abelian variety over a number field k and F a finite cyclic extension of k of ppower degree for an odd prime p. Under certain technical hypotheses, we obtain a reinterpretation of the equivariant Tamagawa number conjecture (`eTNC') for A, F/k and p in terms of explicit padic congr ..."
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adic congruences involving values of derivatives of the HasseWeil Lfunctions of twists of A, normalised by completely explicit twisted regulators. This reinterpretation makes the eTNC amenable to numerical verification and furthermore leads to explicit predictions which refine wellknown conjectures of Mazur
ON THE LOWLYING ZEROS OF HASSEWEIL LFUNCTIONS FOR ELLIPTIC CURVES
, 708
"... Abstract. In this paper, we obtain an unconditional density theorem concerning the lowlying zeros of HasseWeil Lfunctions for a family of elliptic curves. From this together with the Riemann hypothesis for these Lfunctions, we infer the majorant of 241/122 (which is strictly less than 2) for the ..."
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Cited by 3 (2 self)
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Abstract. In this paper, we obtain an unconditional density theorem concerning the lowlying zeros of HasseWeil Lfunctions for a family of elliptic curves. From this together with the Riemann hypothesis for these Lfunctions, we infer the majorant of 241/122 (which is strictly less than 2
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 507 (2 self)
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; for abelian varieties. This result was first proved independently in char. o by Grothendieck, using methods of etale cohomology (private correspondence with J. Tate), and by Mumford, applying the easy half of Theorem (2.5), to go from curves to abelian varieties (cf. [M2]). Grothendieck has recently
THE WARINGGOLDBACH PROBLEM UNDER THE HASSEWEIL HYPOTHESIS
"... exceptions, all positive integers up to N satisfying some necessary congruence conditions, are sums of four cubes of primes; and that every sufficiently large odd integer N with N 6 ≡ 0(mod9) is the sum of seven cubes of primes. 1991 Mathematics Subject Classification. 11P32, 11P05, 11P55. 1. ..."
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exceptions, all positive integers up to N satisfying some necessary congruence conditions, are sums of four cubes of primes; and that every sufficiently large odd integer N with N 6 ≡ 0(mod9) is the sum of seven cubes of primes. 1991 Mathematics Subject Classification. 11P32, 11P05, 11P55. 1.
Diagonal cycles and Euler systems II: The Birch and SwinnertonDyer conjecture for HasseWeilArtin Lfunctions
"... This article establishes new cases of the Birch and SwinnertonDyer conjecture in analytic rank 0, for elliptic curves over Q viewed over the elds cut out by certain selfdual Artin representations of dimension at most 4. When the associated Lfunction vanishes (to even order 2) at its central p ..."
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Cited by 5 (5 self)
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This article establishes new cases of the Birch and SwinnertonDyer conjecture in analytic rank 0, for elliptic curves over Q viewed over the elds cut out by certain selfdual Artin representations of dimension at most 4. When the associated Lfunction vanishes (to even order 2) at its central
Higher regulators of Fermat curves and values of Lfunctions
, 2007
"... Let X be a smooth projective curve over Q with the genus g and L(H1(X), s) be the HasseWeil Lfunction. In [B1], Beilinson defines a regulator map regD: H ..."
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Let X be a smooth projective curve over Q with the genus g and L(H1(X), s) be the HasseWeil Lfunction. In [B1], Beilinson defines a regulator map regD: H
UncoveringaNew Lfunction
"... announced the computation of some “degree 3 transcendental Lfunctions ” at a workshop 1 ..."
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announced the computation of some “degree 3 transcendental Lfunctions ” at a workshop 1
Results 1  10
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