Results 1 to 10 of about 1,486 (43)
Generalized Dedekind eta-functions and generalized Dedekind sums [PDF]
Transactions of the American Mathematical Society, 1973 A transformation formula under modular substitutions is derived for a very large class of generalized Eisenstein series. The result also gives a transformation formula for generalized Dedekind eta-functions. Various types of Dedekind sums arise, and reciprocity laws are established.
openaire +2 more sources
Elementary proofs of Berndt's reciprocity laws [PDF]
, 1982 Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmetical sums analogous to Dedekind sums. This paper gives elementary proofs of all three reciprocity laws and obtains them all from a common source, a ...
Apostol, Tom M., Vu, Thiennu H.
core +1 more source
On cubic multisections of Eisenstein series [PDF]
, 2013 A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three.
Alaniz, Andrew, Huber, Tim
core +3 more sources
Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series [PDF]
, 2007 We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademacher sums arise. In the course of its proof, we also obtain a transformation formula for elliptic Dedekind-Rademacher sums. When a complex parameter $¥tau$
Machide, Tomoya
core +1 more source
Fractional effective action at strong electromagnetic fields [PDF]
, 2013 In 1936, Weisskopf [K. Dan. Vidensk. Selsk. Mat. Fys. Medd. XIV (1936)] showed that for vanishing electric or magnetic fields the strong-field behavior of the one-loop Euler-Heisenberg effective Lagrangian of quantum electro dynamics (QED) is logarithmic.
Kleinert, Hagen +2 more
core +2 more sources
On the distribution of Dedekind sums [PDF]
, 2017 Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums.
Girstmair, Kurt
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
Records on the vanishing of Fourier coefficients of Powers Of the Dedekind Eta Function
, 2018 In this paper we significantly extend Serre's table on the vanishing properties of Fourier coefficients of odd powers of the Dedekind eta function. We address several conjectures of Cohen and Str\"omberg and give a partial answer to a question of Ono. In
Heim, Bernhard +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 +33 more
core +4 more sources
The partition function of interfaces from the Nambu-Goto effective string theory
, 2006 We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of ...
F. Bursa +31 more
core +1 more source