Proceedings of the Indian Academy of Sciences
Mathematical Sciences


VOL. 104, January-December 1994


Contents

February 1, 1994
Pages
Special issue dedicated to the memory of Professor K. G. Ramanathan

On the equation x(x+d1)...(x+(k-1)d1) = y(y+d2)...(y+(mk-1)d2)..... — N. Saradha and
T. N. Shorey
1-12
The density of rational points on non-singular hypersurfaces — D. R. Heath Brown
13-29
Multiplicative arithmetic of finite quadratic forms over Dedeking rings — Anatoli Andrianov
31-48
Non-surjectivity of the Clifford invariant map — R. Parimala and R. Sridharan
49-56
Modular forms and differential operators — Don Zagier
57-75
On Fourier coefficients of Maass cusp forms in 3-dimensional hyperbolic space — S. Raghavan and J. Sengupta
77-92
On Zagier's cusp form and the Ramanujan function — Ashwaq Hashim and M. Ram Murty
93-98
Zeta functions of prehomogeneous vector spaces with coefficients related to periods of automorphic forms — Fumihiro Sato
99-135
On a problem of G Fejes Toth — R. P. Bambah and A. C. Woods
137-156
The number of idelas in a quadratic field — M. N. Huxley and N. Watt
157-165
On the zeros of a class of generalized Dirichlet series -XIV — R. Balasubramanian and
K. Ramachandra
167-176
Local zeta functions of general quadratic polynomials — Jun-ichi Igusa
177-189
Vector bundles as direct images of line bundles — A. Hirschowitz and M. S. Narasimhan
191-200
Finite arithmetic subgroups of GLn, III — Yoshiyuki Kitaoka
201-206
Reduction theory over global fields — T. A. Springer
207-216
Symplectic structures on locally compact abelian groups and polarizations — R. Ranga Rao
217-223
Modular equations and Ramanujan's Chapter 16, Entry 29 — George E. Andrews
225-235
Gaussian quadrature in Ramanujan's Second Notebook — Richar Askey
237-243
Two remarkable doubly exponential series transformations of Ramanuajn — Bruce C. Berndt and James Lee Hafner
245-252
Kolmogorov's existence theorem for Markov processes in C algebras — B. V. Rajarama Bhat and K. R. Parthasarathy
253-262
Existence theory for linearly elastic shells — Philippe G. Ciarlet
269-278
Absolutely expedient algorithms for learning Nash equilibria — V. V. Phansalkar, P. S. Sastry and M. A. L. Thathachar
279-294
Hierarchic control — J. L. Lions
295-304
May 2, 1994

Bertini theorems for ideals linked to a given ideal — Trivedi Vijaylaxmi
305-331
On the Ramanujan-Petersson conjecture for modular forms of half-integral weight — Winfried Kohnen
333-337
On composition of some general fractional integral operators — K. C. Gupta and R. C. Soni
339-349
On the absolute matrix summability of Fourier series and some associated series — B. K. Ray and A. K. Sahoo
351-366
On a absolute summability factors of infinite series — Huseyin Bor
367-372
Rearrangemetns of bounded variation sequences — Mehmet Ali Sarigol
373-376
A note on a generalization of Macdonald's identities for A and B — N. Sthanumoorthy and
M. Tamba
377-383
Combinatorial manifolds with complementarity — Basudeb Data
385-388
Deformations of complex structures on Sl2(C) — C. S. Rajan
389-395
Differential subordinations concerning starlike functions — S. Ponnusamy
397-411
On the structure of stable random walks — Jon Aaronson
413-419
L(µ, X) as a complemented subspace of its bidual — T. S. S. R. K. Rao
421-424
Stresses in an elastic plate lying over a base due to strip-loading — Raj Kumar Sharma and Nat Ram Garg
425-433
August 3, 1994

The Laplacian on algebraic threefolds with isolated singularities — Vishwambhar Patil
435-481
The Hoffman-Wielandt inequality in infinite dimensions — Rajendra Bhatia and Ludwig Elsner
483-494
Rigidity problem for lattices in solvable Lie groups — A. N. Starkov
495-514
Some remarks on the Jacobian question — Shreeram S. Abhyankar
515-542
On polynomial isotopy of Knot-types — Rama Shukla
543-548
Row-reduction and invariants of Diophantine equations — N. J. Wildberger
549-555
Positive values of non-homogeneous indefinite quadratic forms of type (1,4) — V. C. Dumir and Ranjeet Sehmi
557-579
Extended Kac-Akhiezer formulae and the Fredholm determinant of finite section Hilbert-Schmidt kernels — S. Ganapathi Raman and R. Vittal Rao
581-591
A proof of Howard's conjecture in homogeneous parallel shear flows — Mihir B. Banerjee, R. G. Shandil and Vinay Kanwar
593-595
November 4, 1994

Foreword
597
Scattering theory for Stark Hamiltonians — A. Jensen
599-651
L-Estimates for Schrodinger operators — S. Nakamura
653-666
On N-body Schrodinger operators — H. Isozaki
667-703
A conjecture for some partial differential operators in L(Rn) — Pl. Muthuramalingam
705-714
The geometry and spectra of hyperbolic manifolds — P. D. Hislop
715-776
Inverse spectral theory for Jacobi matrices and their almost periodicity — A. J. Antony and
M. Krishna
777-818
Spectral shift function and trace formula — Kalyan B. Sinha and A. N. Mohapatra
819-853