## 3 Citations

### Proof of generalized Riemann hypothesis for Dedekind zetas and Dirichlet L-functions

- Mathematics
- 2007

A short proof of the generalized Riemann hypothesis (gRH in short) for zeta functions $\zeta_{k}$ of algebraic number fields $k$ - based on the Hecke's proof of the functional equation for…

### Control theory and the Riemann hypothesis: A roadmap

- Mathematics
- 2009

An alternative way of looking at the Riemann hypothesis from the viewpoint of mathematical control theory is considered. A control theoretic transfer function is constructed by inverting the values…

## References

SHOWING 1-10 OF 17 REFERENCES

### The Positivity of a Sequence of Numbers and the Riemann Hypothesis

- Mathematics
- 1997

Abstract In this note, we prove that the Riemann hypothesis for the Dedekind zeta function is equivalent to the nonnegativity of a sequence of real numbers.

### Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

- Mathematics
- 1997

Abstract. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric…

### Hilbert Space: Compact Operators and the Trace Theorem

- Mathematics
- 1993

1. Preliminaries 2. Orthogonality 3. Isomorphisms and isometries 4. Bounded linear operators 5. Elementary spectral theory 6. Self-adjoint operators 7. Compact operators on Hilbert space 8. Square…

### Remarks on Weil’s quadratic functional in the theory of prime numbers, I

- Mathematics
- 2000

— This Memoir studies Weil’s well-known Explicit Formula in the theory of prime numbers and its associated quadratic functional, which is positive semidefinite if and only if the Riemann Hypothesis…

### Problems of the Millennium : the Riemann Hypothesis

- Mathematics, Philosophy
- 2000

with s = 12 + it , and shows that ξ(t) is an even entire function of t whose zeros have imaginary part between −i/2 and i/2. He further states, sketching the proof, that in the range between 0 and T…

### A Treatise on the Theory of Bessel Functions

- PhysicsNature
- 1945

THE memoir in which Bessel, the astronomer, examined in detail the functions which now bear his name was published in 1824, and was the outcome of his earlier researches concerning the expression of…

### SUR LES FORMULES EXPLICITES DE LA THÉORIE DES NOMBRES

- Mathematics
- 1972

"Explicit formulas" in number theory express the sum of values of a function at the zeros of an L-series of an algebraic number field as a sum of local terms corresponding to all norms of this field.…

### An Introduction to Abstract Harmonic Analysis

- Computer Science
- 1953

An introduction to abstract harmonic analysis is one of the literary work in this world in suitable to be reading material and it will show you the amazing benefits of reading a book.