— We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree n and weight k > n/2 has meromorphic continuation to C. Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight k > n/2 may be expressed in terms of the residue at s = k of the associated Dirichlet series....

Arithmetic inner product formula for unitary groups

This paper proposes the first inner product encryption (IPE) scheme that is adaptively secure and fully attribute-hiding (attribute-hiding in the sense of the definition by Katz, Sahai and Waters), while the existing IPE schemes are either fully attribute-hiding but selectively secure or adaptively secure but weakly attribute-hiding. The proposed IPE scheme is proven to be adaptively secure and...

It is well known that for the Hilbert space H the minimum value of the functional Fμ(f) = ∫ H ‖f−g‖2dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H. We show that the validity of this property for measures on a normed space having support at three points with norm 1 and arbitrarily fixed positive weights implies the existence of an inner pro...

We onsider ”Riesz Theorem” in the 2-inner product spaces and give some results in this field. Also, we give some characterizations about 2-inner product spaces in b-approximation theory. AMS Mathematics Subject Classification (2000): 41A65, 41A15

has been introduced by several authors like Ahmed and Hamouly [1], Kohli and Kumar [5], Biswas [4], etc. Also the notion of fuzzy norm on a linear space was introduced by Katsaras [9]. Later on many other mathematicians like Felbin [3], Cheng and Mordeso [10], Bag and Samanta [6], etc, have given different definitions of fuzzy normed spaces. In recent past lots of work have been done in the top...

The notion of inner-product encryption (IPE), introduced by Katz, Sahai, and Waters at Eurocrypt 2008, is a generalization of identity-based encryption in which ciphertexts and secret keys are associated to vectors in some finite field. In an IPE scheme, a ciphertext can only be decrypted by a secret key if the vector associated with the latter is orthogonal to that of the ciphertext. In its hi...

Bayesian networks have become one of the major models used for statistical inference. We study the question whether the decisions computed by a Bayesian network can be represented within a low-dimensional inner product space. We focus on two-label classification tasks over the Boolean domain. As main results we establish upper and lower bounds on the dimension of the inner product space for Bay...

1 Background We begin by recalling the solution of the vibrating string problem and Sturm-Liouville problems. When we solve the problem of the vibrating string using the technique of separation of variables, the differential equation involving the space variable x, and assuming constant mass density, is y (x) + ω 2 c 2 y(x) = 0, (1.1) which we can write as an eigenvalue problem y (x) + λy(x) = ...

In a functional encryption scheme, secret keys are associated with functions and ciphertexts are associated with messages. Given a secret key for a function f and a ciphertext for a message x, a decryptor learns f(x) and nothing else about x. Inner product encryption is a special case of functional encryption where both secret keys and ciphertexts are associated with vectors. The combination of...