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Locally harmonic Maass forms and rational period functions
hyperbolic Poincare series harmonic weak Maass forms cusp forms lifting maps Shimura lift Shintani lift
2012/6/21
In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier which played an important ...
Quadratic congruences on average and rational points on cubic surfaces
Quadratic congruences rational points Manin’s conjecture cubic surfaces universal torsors
2012/5/24
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
Counting rational points over number fields on a singular cubic surface
rational points over number fields singular cubic surface Number Theory
2012/4/18
A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successful...
Rational approximations to values of Bell polynomials at points involving Euler's constant and zeta values
Bell polynomials Euler's constant zeta values
2010/11/22
In this paper, we present new explicit simultaneous rational approximations converging sub-exponentially to the values of Bell polynomials at the points of the form $(\gamma, 1! (2a+1)\zeta(2), 2!\zet...
Gromov-Witten invariants and rational curves on Grassmannians
Gromov-Witten invariants rational curves on Grassmannians
2010/11/15
We study the enumerative significance of the s-pointed genus zero Gromov-Witten invariant on a homogeneous space X. For that, we give an interpretation in terms of rational curves on X.