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Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
Lehmer's conjecture Hermitian matrices Eisenstein and Gaussian integers Number Theory
2012/6/29
We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least ...
On higher congruences between cusp forms and Eisenstein series
higher congruences cusp forms Eisenstein series Number Theory
2012/6/30
In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properti...
An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions
the zero-counting formulae Dirichlet $L$-functions Dedekind zeta-functions Number Theory
2012/6/30
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.
Distinct zeros and simple zeros of Dirichlet $L$-functions
simple zeros distinct zeros Dirichlet L-function
2012/6/29
We study the number of distinct zeros and simple zeros of Dirichlet $L$-function by using Asymptotic Large Sieve in this paper. In asymptotic terms, we prove that there are more than 66.43% of zeros o...
An integer $n$ is said to be \textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we char...
Examples of abelian surfaces with non-square Tate-Shafarevich group
Examples of abelian surfaces non-square Tate-Shafarevich group Number Theory
2012/6/30
In this article we show the existence of abelian surfaces over Q with Tate-Shafarevich groups having orders five times a square and seven times a square. To obtain this result, we explore the invarian...
The local-global exact sequence for Chow groups of zero-cycles
zero-cycles local-global principle Brauer–Manin obstruction
2012/6/27
A local-global sequence for Chow groups of zero-cycles involving Brauer groups has been conjectured to be exact for all proper smooth algebraic varieties. We apply existing methods to construct severa...
A Cohen-Lenstra phenomenon for elliptic curves
A Cohen-Lenstra phenomenon elliptic curves Number Theory
2012/6/29
Given an elliptic curve $E$ and a finite Abelian group $G$, we consider the problem of counting the number of primes $p$ for which the group of points modulo $p$ is isomorphic to $G$. Under a certain ...
Linear Mahler Measures and Double L-values of Modular Forms
Linear Mahler Measures Double L-values of Modular Forms Number Theory
2012/6/27
We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a ...
We give a congruence for L-functions coming from affine additive exponential sums over a finite field. Precisely, we give a congruence for certain operators coming from Dwork's theory. This congruence...
Explicit constructions of extractors and expanders
Explicit constructions extractors and expanders Number Theory
2012/6/21
We investigate 2-variable expanders and 3-source extractors in prime fields. We extend previous results of J. Bourgain.
Density of crystalline points on unitary Shimura varieties
Density of crystalline points unitary Shimura varieties Number Theory
2012/6/25
We prove that crystalline points are dense in the spectrum of the completed Hecke algebra on unitary Shimura varieties.
Random Galois extensions of Hilbertian fields
Random Galois extensions Hilbertian fields Number Theory
2012/6/21
Let L be a Galois extension of a countable Hilbertian field K. Although L need not be Hilbertian, we prove that an abundance of large Galois subextensions of L/K are.
From etale $P_{+}$-representations to $G$-equivariant sheaves on $G/P$
From etale $P_{+}$-representations $G$-equivariant sheaves $G/P$ Number Theory
2012/6/21
Let $K/\mathbb Q_{p}$ be a finite extension with ring of integers $o$, let $G$ be a connected reductive split $\mathbb Q_{p}$-group of Borel subgroup $P=TN$ and let $\alpha$ be a simple root of $T$ in...
On a completed generating function of locally harmonic Maass forms
locally harmonic Maass forms indefinite theta functions holomorphic projection mock modular forms modular forms
2012/6/21
While investigating the Doi-Naganuma lift, Zagier defined integral weight cusp forms $f_D$ which are naturally defined in terms of binary quadratic forms of discriminant $D$. It was later determined b...