ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 07 Dec 2022 10:31:20 GMT2022-12-07T10:31:20Z5091- Abelian divisible difference sets with multiplier -1https://scholarbank.nus.edu.sg/handle/10635/102790Title: Abelian divisible difference sets with multiplier -1
Authors: Leung, K.H.; Ma, S.L.; Tan, V.
Abstract: We investigate (m, n, k, λ1, λ2)-divisible difference sets in an abelian group admitting -1 as a multiplier. For the reversible case, we show that this assumption implies severe restrictions on the structure of divisible difference sets. In particular, if (λ1 - λ2)n + k - λ1 is not a square, we prove that all the corresponding divisible difference sets can be constructed by using certain partial difference sets. Also, we determine the structure of reversible divisible difference sets if a Sylow subgroup of G is cyclic. As a consequence, we completely characterize all reversible divisible difference sets in cyclic groups. Finally, the case that -1 is a weak multiplier is studied and restrictions on the parameters are obtained. In fact, we show that n must be a power of 2. © 1992.
Wed, 01 Jan 1992 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1027901992-01-01T00:00:00Z
- An application of the regularized siegel-weil formula on unitary groups to a theta lifting problemhttps://scholarbank.nus.edu.sg/handle/10635/102819Title: An application of the regularized siegel-weil formula on unitary groups to a theta lifting problem
Authors: Tan, V.
Abstract: Let U(2) and U(2,1) be the pair of unitary groups over a global field F and IT an irreducible cuspidal representation of U(2) which satisfies a certain L-function condition. By using a regularized Siegel-Weil formula, we can show that the global theta lifting of TT in U(2,1) is non-trivial if every local factor πν of π has a local theta lifting (Howe lifting) in U(2, i)(Fv). © 1999 American Mathematical Society.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1028191999-01-01T00:00:00Z
- A regularized Siegel-Weil formula on U(2, 2) and U(3)https://scholarbank.nus.edu.sg/handle/10635/102746Title: A regularized Siegel-Weil formula on U(2, 2) and U(3)
Authors: Tan, V.
Sat, 15 Aug 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1027461998-08-15T00:00:00Z
- Intertwining Operators for Vertex Representations of Toroidal Lie Algebrashttps://scholarbank.nus.edu.sg/handle/10635/103439Title: Intertwining Operators for Vertex Representations of Toroidal Lie Algebras
Authors: Lum, K.H.; Tan, V.
Abstract: The construction of the vertex representation of the toroidal Lie algebra τ[n] depends on the way of labelling the points in the dual ℤn of the torus Tn. Thus there is a built-in symmetry of the vertex representation with respect to the symmetry of ℤn. In conjunction with this, the energy operator L0 gives rise to intertwining operators which reflect the symmetry of the vertex representation with respect to S1 action on τ[n].
Sat, 01 Aug 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034391998-08-01T00:00:00Z
- Poles of Siegel Eisenstein series on U (n, n)https://scholarbank.nus.edu.sg/handle/10635/103944Title: Poles of Siegel Eisenstein series on U (n, n)
Authors: Tan, V.
Abstract: Let U (n, n) be the rank n quasi-split unitary group over a number field. We show that the normalized Siegel Eisenstein series of U (n, n) has at most simple poles at the integers or half integers in certain strip of the complex plane.
Mon, 01 Feb 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039441999-02-01T00:00:00Z
- Planar Functions from Z n to Z nhttps://scholarbank.nus.edu.sg/handle/10635/103937Title: Planar Functions from Z n to Z n
Authors: Leung, K.H.; Ma, S.L.; Tan, V.
Abstract: In this paper, we show that there are no planar functions from Z3pq to Z3pq where p and q are distinct primes larger than 3. As a result, there are only two undecided cases for planar functions from Zn to Zn if n is not a prime and n≤50,000. © 2000 Academic Press.
Tue, 15 Feb 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039372000-02-15T00:00:00Z
- Ramanujans class invariant λn and a new class of series for 1/πhttps://scholarbank.nus.edu.sg/handle/10635/104019Title: Ramanujans class invariant λn and a new class of series for 1/π
Authors: Chan, H.H.; Liaw, W.-C.; Tan, V.
Abstract: On page 212 of his lost notebook, Ramanujan defined a new class invariant λn and constructed a table of values for λn. The paper constructs a new class of series for 1/π associated with λn. The new method also yields a new proof of the Borweins general series for 1/π belonging to Ramanujans theory of q2. © London Mathematical Society 2001.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1040192001-01-01T00:00:00Z
- Cubic singular moduli, Ramanujan's class invariants λn and the explicit shimura reciprocity lawhttps://scholarbank.nus.edu.sg/handle/10635/103089Title: Cubic singular moduli, Ramanujan's class invariants λn and the explicit shimura reciprocity law
Authors: Chan, H.H.; Gee, A.; Tan, V.
Abstract: In this paper, we use the explicit Shimura Reciprocity Law to compute the cubic singular moduli α*n, which are used in the constructions of new rapidly convergent series for 1/π. We also complete a table of values for the class invariant λn initiated by S. Ramanujan on page 212 of his Lost Notebook.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030892003-01-01T00:00:00Z
- On determinant preserver problemshttps://scholarbank.nus.edu.sg/handle/10635/103699Title: On determinant preserver problems
Authors: Tan, V.; Wang, F.
Abstract: Let Mn and Tn be the vector spaces of n×n matrices and upper triangular matrices over a field F (with some cardinality and characteristic restrictions) respectively. We characterise transformations φ on these two spaces separately which satisfy one of the following conditions: det(A+λB)=det(φ(A)+λφ(B)) for all A, B and λ. φ is surjective and det(A+λB)=det(φ(A)+λφ(B)) for all A, B and two specific λ. φ is additive and preserves determinant. © 2003 Elsevier Science Inc. All rights reserved.
Fri, 01 Aug 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1036992003-08-01T00:00:00Z