23 citations · 57 across the 17 of their papers we have counts for
19 papers
The Shimura Lift and Hilbert Modular Forms
Henri Cohen
After recalling basic formulas concerning modular forms of half-integral weight, Gegenbauer polynomials, and Rankin--Cohen brackets, we give four versions of the Shimura lift and s…
On the Argument of the Lerch, Chowla--Selberg Formula and CM Values of
Henri Cohen
We give a completely explicit Lerch, Chowla--Selberg formula without absolute values of the Dedekind eta function, and give some applications, in particular to the argument of indi…
Parametric Continued Fractions for , , and other Constants
Henri Cohen
We give an extensive list of parametrized families of polynomial continued fractions of smallest possible degrees for and , and mention similar results for other consta…
Elementary Continued Fractions for Linear Combinations of Zeta and L Values
Henri Cohen
We show how to obtain infinitely many continued fractions for certain Z-linear combinations of zeta and L values. The methods are completely elementary.
Factorizations of Eisenstein Series of Level up to 4
Henri Cohen
We show that the most standard Eisenstein series such as or , and also the function , are in a natural way the product of two conjugate Eisenstein…
Rational Hypergeometric Ramanujan Identities for : Survey and Generalizations
Henri Cohen, Jesús Guillera
We give a simple unified proof for all existing rational hypergeometric Ramanujan identities for , and give a complete survey (without proof) of several generalizations: ratio…
Computing L-Functions of Quadratic Characters at Negative Integers
Henri Cohen
We survey a number of different methods for computing for a Dirichlet character , with particular emphasis on quadratic characters. The main conclusion is that when $…
Lambert -Function Branch Identities
Henri Cohen
After defining in detail the Lambert -function branches, we give a large number of exact identities involving (infinite) symmetric functions of these branches, as well as geomet…
Modular Forms in Pari/GP
Karim Belabas, Henri Cohen
We give theoretical and practical information on the Pari/GP modular forms package available since the spring of 2018. Thanks to the use of products of two Eisenstein series, this…
Expansions at Cusps and Petersson Products in Pari/GP
Henri Cohen
We begin by explaining how to compute Fourier expansions at all cusps of any modular form of integral or half-integral weight thanks to a theorem of Borisov-Gunnells and explicit e…
An Introduction to Modular Forms
Henri Cohen
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with…
Computational Number Theory in Relation with L-Functions
Henri Cohen
We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving…
On -extensions of odd prime degree
Henri Cohen, Frank Thorne
Generalizing the work of A. Morra and the authors, we give explicit formulas for the Dirichlet series generating function of -extensions of odd prime degree with g…
Finite hypergeometric functions
Frits Beukers, Henri Cohen, Anton Mellit
Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz i…
Dirichlet series associated to cubic fields with given quadratic resolvent
Henri Cohen, Frank Thorne
Let k be a quadratic field. We give an explicit formula for the Dirichlet series enumerating cubic fields whose quadratic resolvent field is isomorphic to k. Our work is a sequel t…
Counting Cubic Extensions with given Quadratic Resolvent
Henri Cohen, Anna Morra
Given a number field and a quadratic extension , we give an explicit asymptotic formula for the number of isomorphism classes of cubic extensions of whose Galois closu…
Elementary 3-descent with a 3-isogeny
Henri Cohen, Fabien Pazuki
In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and…
Computational class field theory
Henri Cohen, Peter Stevenhagen
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algor…
Constructing and counting number fields
Henri Cohen
In this paper we give a survey of recent methods for the asymptotic and exact enumeration of number fields with given Galois group of the Galois closure. In particular, the case of…