Derivative formulas for hermitian theta functions of degree two

Somos Sequence Near-Addition Formulas and Modular Theta Functions

We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.

Comparing two Formulas of Sample Size Determination for Prevalence Studies

Background and purpose: Sample size and its determination is one of the most important problems in health researches. Calculating sample size for prevalence studies is one of the common questions of sample size topics. Minimum sample size with least complexity is desirable in order to achieve the basic goal of these studies. This study aims to compare two formulas of sample size calculation for...

Theta functions on covers of symplectic groups

We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$‎. ‎This representation is obtained from the residues of Eisenstein series on this group‎. ‎If $r$ is odd‎, ‎$nle r

Factorization of rank two theta functions

On Two Fifth Order Mock Theta Functions

We consider the fifth order mock theta functions χ0 and χ1, defined by Ramanujan, and find identities for these functions, which relate them to indefinite theta functions. Similar identities have been found by Andrews for the other fifth order mock theta functions and the seventh order functions.