At the 1991 West Coast Number Theory Conference, Emma Lehmer asked for proofs of the formulas on semi-symmetric cyclotomic sums that appeared without proof in D. H. Lehmer's last notebook. This note is the result. Furthermore, we show how to determine signs which Lehmer had left ambiguous. Classical cyclotomy defined the cyclotomic classes of degree e and prime conductor p = ef + 1 to be (1) C ...

We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function field and its kinetic term there also k-essence consisting term. This has three frames that are equivalent one another: original Jordan frame, Einstein frame metric redefined, Riemann connection redefined. For first t...

with using antibiotic in societies which usage of this kind of the drug without any limitation cause appear resistance against antibiotics.this survey consider to use the extract and essence of the cinnamon (which have a so many rate of planting in iran) and also survey on extract on bacteria whose cause urinary tract infections, and compare this with common antibiotics. this study was experime...

For prime power q = p and a field F containing a root of unity of order q we show that the Galois cohomology ring H∗(GF , Z/q) is determined by a quotient G [3] F of the absolute Galois group GF related to its descending q-central sequence. Conversely, we show that G [3] F is determined by the lower cohomology of GF . This is used to give new examples of pro-p groups which do not occur as absol...

Abstract. Concerning the uniqueness and sharing values of meromorphic functions, many results about meromorphic functions that share more than or equal to two values have been obtained. In this paper, we shall study meromorphic functions that share only one value, and prove the following result: For n ≥ 11 and two meromorphic functions f(z) and g(z) , if ff ′ and gg share the same nonzero and f...

In [l] Bagchi and Bagchi conjectured that one of the hypotheses of their theorem 2(d) is superfluous. This turns out to be true: PROPOSITION. Let 4 = 9 mod 16 be a prime power such that 2 is a fourth power in Fq. Then 1 f fi are nonsquares in Fp. Pruc$ Let p be a primitive eighth root of unity in Fq (note that /3 is a nonsquare). Because of (02 + 1)2 = p4 + 202 + 1 = 202 we obtain that (0 * + 1...

Single mass scale diagrams: construction of a basis for the ε-expansion. Abstract Exploring the idea of Broadhurst on the " sixth root of unity " we present an ansatz for construction of a basis of transcendental numbers for the ε-expansion of single mass scale diagrams with two particle massive cut. As example, several new two-and three-loop master integrals are calculated.

As usual, we write Z,Q,Fp,C for the ring of integers, the field of rational numbers, the finite field with p elements and the field of complex numbers respectively. If Z is a smooth algebraic variety over an algebraically closed field then we write Ω(Z) for the space of differentials of the first kind on Z. If Z is an abelian variety then we write End(Z) for its ring of (absolute) endomorphisms...

We prove a Morita reduction theorem for the cyclotomic Hecke algebras Hr,p,n(q,Q) of type G(r, p, n). As a consequence, we show that computing the decomposition numbers of Hr,p,n(Q) reduces to computing the psplittable decomposition numbers (see Definition 1.1) of the cyclotomic Hecke algebras Hr′,p′,n′ (Q ), where 1 ≤ r ≤ r, 1 ≤ n ≤ n, p | p and where the parameters Q are contained in a single...