29,367 research outputs found

    B\"acklund transformations for nonlinear evolution equations: Hilbert space approach

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    A new method of determining B\"acklund transformations for nonlinear partial differential equations of the evolution type is introduced. Using the Hilbert space approach the problem of finding B\"acklund transformations is brought down to the solution of an abstract equation in Hilbert space.Comment: 15 page

    Amplification arguments for large sieve inequalities

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    We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea. We show that this also adapts to give some new sieve inequality for modular forms, where Hecke eigenvalues are thought as the analogues of the reductions of integers modulo primes.Comment: 13 pages, 1 figure; v2, version accepted for publication in Archiv der Math

    Weil numbers generated by other Weil numbers and torsion fields of abelian varieties

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    Using properties of the Frobenius eigenvalues, we show that, in a precise sense, ``most'' isomorphism classes of (principally polarized) simple abelian varieties over a finite field are characterized up to isogeny by the sequence of their division fields, and a similar result for ``most'' isogeny classes. Some global cases are also treated.Comment: 13 page
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