Results 11 to 20 of about 1,484 (43)

Identities for generalized Appell functions and the blow-up formula

, 2015
In this paper, we prove identities for a class of generalized Appell functions which are based on the $\operatorname{A}_2$ root lattice. The identities are reminiscent of periodicity relations for the classical Appell function, and are proven using only ...
Bringmann, Kathrin, Manschot, Jan, Rolen, Larry   +2 more
core   +1 more source

Seiberg--Witten invariants and surface singularities

, 2001
We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we establish its validity
András Némethi, Arnol’d, Chen, Collin, Gompf, Greuel, Hirzebruch, Hirzebruch, Ishii, Jankins, Laufer, Lescop, Lim, Liviu I Nicolaescu, Marcolli, Mrowka, Neumann, Neumann, Neumann, Nicolaescu, Nicolaescu, Nicolaescu, Nicolaescu, Nicolaescu, Némethi, Némethi, Rademacher, Rademacher, Steenbrink, Séade, Turaev, Turaev, van der Blij, Walker   +33 more
core   +4 more sources

On Eisenstein series in $M_{2k}(\Gamma_0(N))$ and their applications

, 2018
Let $k,N \in \mathbb{N}$ with $N$ square-free and $k>1$. We prove an orthogonal relation and use this to compute the Fourier coefficients of the Eisenstein part of any $f(z) \in M_{2k}(\Gamma_0(N))$ in terms of sum of divisors function. In particular, if
Aygin, Zafer Selcuk
core   +1 more source

On the Quantum Invariant for the Brieskorn Homology Spheres

, 2005
We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev invariant for the Brieskorn homology spheres $\Sigma(p_1,p_2,p_3)$ by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that
Abramowitz M., Fintushel R., Freed D. S., Hikami K., KAZUHIRO HIKAMI, Lang S., Mordell L. J., Rademacher H., Walker K.   +8 more
core   +1 more source

Einstein metrics and Yamabe invariants of weighted projective spaces

, 2013
An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics.
Viaclovsky, Jeff A.
core   +1 more source

Transformation laws for generalized Dedekind sums associated to Fuchsian groups

, 2019
We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples
Burrin, Claire, Jorgenson, Jay, O'Sullivan, Cormac, Smajlović, Lejla   +3 more
core  

Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. [PDF]

Math Ann, 2023
Minelli P, Sourmelidis A, Technau M.
europepmc   +1 more source

On the infinite Borwein product raised to a positive real power. [PDF]

Ramanujan J, 2023
Schlosser MJ, Zhou NH.
europepmc   +1 more source

From partitions to Hodge numbers of Hilbert schemes of surfaces. [PDF]

Philos Trans A Math Phys Eng Sci, 2020
Gillman N, Gonzalez X, Ono K, Rolen L, Schoenbauer M.   +4 more
europepmc   +1 more source

On a hybrid mean value of certain Hardy sums and Ramanujan sum [PDF]

, 2003
Zhang, Wenpeng
core   +2 more sources