A Residue Scalar Product for Algebraic Function Fields over a Number Field
نویسنده
چکیده
In 1953 Peter Roquette gave an arithmetic proof of the Riemann hypothesis for algebraic function fields over a finite constants field, which was proved by André Weil in 1940. The construction of Weil’s scalar product is essential in Roquette’s theory. In this paper a scalar product for algebraic function fields over a number field is constructed which is the analogue of Weil’s scalar product.
منابع مشابه
HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
متن کاملCasimir effects of nano objects in fluctuating scalar and electromagnetic fields: Thermodynamic investigating
Casimir entropy is an important aspect of casimir effect and at the nanoscale is visible. In this paper, we employ the path integral method to obtain a general relation for casimir entropy and internal energy of arbitrary shaped objects in the presence of two, three and four dimension scalar fields and the electromagnetic field. For this purpose, using Lagrangian and based on a perturb...
متن کاملAlgebraic adjoint of the polynomials-polynomial matrix multiplication
This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field
متن کاملSimulation of Low Reynolds Number Isotropic Turbulence Including the Passive Scalar
Full simulations of homogeneous isotropic turbulence containing a homogeneous passive scalar were made at low Reynolds numbers and various Prandtl numbers. The results show that the spectral behavior of the two fields are quite similar; both fields decay as power-law functions of time. However. the decay exponent is quite dependent on both the Reynolds and Prandtl numbers. The decay exponent of...
متن کاملA high speed coprocessor for elliptic curve scalar multiplications over Fp
We present a new hardware architecture to compute scalar multiplications in the group of rational points of elliptic curves defined over a prime field. We have made an implementation on Altera FPGA family for some elliptic curves defined over randomly chosen ground fields offering classic cryptographic security level. Our implementations show that our architecture is the fastest among the publi...
متن کامل