The growth rate of the Dedekind Zeta-function on the critical line
The Hasse conjecture for cyclic extensions.
The Hasse norm principle in cyclotomic number fields.
The Hasse norm principle in non-abelian extensions.
The Hasse Principle modulo nth powers
The Hasse-Witt invariant of cyclotomic function fields
The Hasse-Witt Matrix of a Formal Group.
The Heegner-Stark-Baker-Deuring-Siegel Theorem.
The Hilbert-Kunz Function.
The homology of cyclic branched covers of S3.
The homology of irregular dihedral branched covers of S3.
The Hooley-Huxley contour method for problems in number fields III : frobenian functions
In this paper we study finite valued multiplicative functions defined on ideals of a number field and whose values on the prime ideals depend only on the Frobenius class of the primes in some Galois extension. In particular we give asymptotic results when the ideals are restricted to “small regions”. Special cases concern Ramanujan's tau function in small intervals and relative norms in “small regions” of elements from a full module of the Galois extension.
The Image of the Atiyah-Bott Map.
The imaginary abelian number fields with class numbers equal to their genus class numbers
We know that there exist only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Such non-quadratic cyclic number fields are completely determined in [Lou2,4] and [CK]. In this paper we determine all non-cyclic abelian number fields with class numbers equal to their genus class numbers, thus the one class in each genus problem is solved, except for the imaginary quadratic number fields.
The imaginary bicyclic biquadratic fields with class-number 1.
The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic sextic fields with class numbers equal to their genus class numbers.
The imaginary quadratic fields of class number 4
The Index of Stickelberger Ideals of Order2 and Cuspidal Class Numbers .
The integer Chebyshev constant of Farey intervals.
We obtain new bounds for the integer Chebyshev constant of intervals [p/q, r/s] where p, q, r and s are non-negative integers such that qr - ps = 1. As a consequence of the methods used, we improve the known lower bound for the trace of totally positive algebraic integers.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
The integer transfinite diameter of intervals and totally real algebraic integers
In this paper we build on some recent work of Amoroso, and Borwein and Erdélyi to derive upper and lower estimates for the integer transfinite diameter of small intervals , where is a fixed rational and . We also study functions associated with transfinite diameters of Farey intervals. Then we consider certain polynomials, which we call critical polynomials, associated to a given interval . We show how to estimate from below the proportion of roots of an integer polynomial which is sufficiently...