An inequality for Fibonacci numbers
We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.
An inequality for local unitary Theta correspondence
Given a representation of a local unitary group and another local unitary group , either the Theta correspondence provides a representation of or we set . If is fixed and varies in a Witt tower, a natural question is: for which is ? For given dimension there are exactly two isometry classes of unitary spaces that we denote . For let us denote the minimal of the same parity of such that , then we prove that where is the dimension of .
An inequality for the class number.
An infinite dimensional Hodge-Tate theory
An infinite family of dual sequence identities.
An infinite family of elliptic curves over Q with large rank via Néron's method.
An infinite family of graphs with the same Ihara Zeta function.
An infinite family of overpartition congruence modulo 12.
An infinite family of pairs of quadratic fields ℚ(√D) and ℚ(√mD) whose class numbers are both divisible by 3
An infinite family of totally real number fields
An infinite ferm in the universal deformation space of Galois representations.
I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks to some...
An infinite product with bounded partial quotients
An integral basis of the algebraic number field Q(...).
An integral involving the generalized zeta function.
An integral involving the remainder term in the Piltz divisor problem
An integral recurrence for sums of powers.
An integral representation of standard automorphic functions for unitary groups.
An integral transform and its applications.
An integrality criterion for elliptic modular forms
Let be an elliptic modular form level of N. We present a criterion for the integrality of at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to the iterates of the Maaß differential operators.
An interesting family of curves of genus 1.