In this paper we show that, under the assumption that all the zeros of the L-functions under consideration are either real or lie on the critical line, one may considerably improve on the known results on Landau-Siegel zeros.

The purpose of this paper is to investigate the real sequences γ0, γ1, γ2, . . . with the property that if p(x) = ∑n k=0 akx k is any real polynomial, then ∑n k=0 γkakx k has no more nonreal zeros than p(x). In particular, the authors establish a converse to a classical theorem of Laguerre.

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This is a continuation of the papers of Braun and Fløystad [BF] and Cook [C] bounding the degree of smooth surfaces not of general type in P 4. We will prove the following: Theorem 1. Let S be a smooth surface of degree d in P 4 not of general type. Then d ≤ 66. The new idea in this paper is to bound the degree of the sporadic zeros of a generic hyperplane section of the surface by considering ...

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval (−1, 1) are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random p...

For a given real entire function φ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions Q = (φ/φ) and Q1 = (φ /φ). This connection leads to a proof of the Hawaii conjecture [T.Craven, G.Csordas, and W. Smith, The zeros of derivatives of entire functions and the Pólya-Wiman conjecture, Ann. of Math. (2) 125 (1987), 405–431] stating that th...

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Let E be an elliptic curve defined over Q and with complex multiplication by OK , the ring of integers in an imaginary quadratic field K. Let p be a prime of good reduction for E. It is known that E(Fp) has a structure (1) E(Fp) ' Z/dpZ⊕ Z/epZ with uniquely determined dp|ep. We give an asymptotic formula for the average order of ep over primes p ≤ x of good reduction, with improved error term O...

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Abstract: Necessary and sufficient conditions for the reachability and observability of the positive electrical circuits composed of resistors, coils, condensators and voltage sources are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros of the positive electrical circuits are proposed. Some properties of the decoupling zeros of po...