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Regulators of K1 of Hypergeometric Fibrations
We study a deformation of what we call hypergeometric fibrations. Its periods and K1-regulators are described in terms of hypergeometric functions...
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Unconditional construction of K3 surfaces over finite fields with given L-function in large characteristic
We give an unconditional construction of K 3 surfaces over finite fields with given L -function, up to finite extensions of the base fields, under some...
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CM fields of Dihedral type and the Colmez conjecture
In this paper, we consider some CM fields which we call of dihedral type and compute the Artin L -functions associated to all CM types of these CM...
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On the distribution of torsion points modulo primes: the case of function fields
We derive an analogue, in the setting of function fields, of a result (Chen–Kuan) on the distribution of torsion points in commutative algebraic...
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The cubic Fermat equation and complex multiplication on the Deuring normal form
The arithmetic on elliptic curves in Deuring normal form is shown to be related to solutions of the Fermat equation 27 X 3 +27 Y 3 = X ...
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Eisenstein series for SL(2)
This paper gives explicit formulas for the Fourier expansion of general Eisenstein series and local Whittaker functions over SL 2 . They are used to...
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On automorphisms of principally polarized abelian varieties
Let ( X , H ) be a g -dimensional principally polarized abelian variety (p.p.a.v.) and Aut( X , H ) its group of automorphisms, in this brief survey we...
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Algebraic Values of Schwarz Triangle Functions
We consider Schwarz maps for triangles whose angles are rather general rational multiples of π. Under which conditions can they have algebraic values...
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On the Blaschke conjecture for 3-webs
We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and...
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On the 0-dimensional irreducible components of the singular locus of \(\mathcal{A}_g\)
In this short note we give a characterization of extremal principally polarized abelian varieties determining an isolated point in Sing
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A Hyperelliptic Curve with Real Multiplication of Degree Two
The analogue of complex multiplication in an elliptic curve is illustrated for a hyperelliptic curve with real multiplication of degree two (over C)....
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Determination of All Q-Rational CM-Points in Moduli Spaces of Polarized Abelian Surfaces
It is known that in the moduli space A l of elliptic curves, there exist precisely 9 Q-rational points corresponding to the isomorphism...
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Integral and modular representations attached to the Selmer group of an elliptic curve with complex multiplication
Let E be an elliptic curve with complex multiplication over the ring of integers of an imaginary quadratic field K . Denote by p an odd prime that...
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Special Points on the Product of Two Modular Curves
We prove, assuming the generalized Riemann hypothesis for imaginary quadratic fields, the following special case of a conjecture of Oort, concerning...
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Parameter spaces for complex tori with endomorphism structure
A nondegenerate complex torus is a pair consisting of a complex torus X and a class H of nondegenerate line bundles on X . We give necessary...