31. Riemann used theta functions in several variables and reduced the problem to the determination of the zeros of these theta functions. 32. Riemann used theta functions in several variables and reduced the problem to the determination of the zeros of these theta functions . 33. The main techniques are the Jacobi theta functions and the construction of a new class of elliptic operators associated to foliations. 34. He proved the functional equation for the zeta function ( already known to Euler ), behind which a theta function lies. 35. The fourth theta function and thus the others too is intimately connected to the Jackson-gamma function via the relation 36. The Jacobi theta function is then a special case, with 1 } } and where is the upper half-plane. 37. Where \ theta _ { m } and \ vartheta _ { ij } are alternative notations for the Jacobi theta functions . 38. The image of Gaussian functions under the Weil Brezin map are nil-theta functions , which are related to theta functions. 39. The image of Gaussian functions under the Weil Brezin map are nil-theta functions, which are related to theta functions . 40. We see that the theta functions can also be defined in terms of and, without a direct reference to the exponential function.
