Signatures of the Kondo effect in the electrical conductance of strongly correlated quantum dots are well understood both experimentally and theoretically, while those in the thermopower have been the subject of recent interest, both theoretically and experimentally. Here, we extend theoretical work [T. A. Costi, Rev. B 100. 161106 (2019)] on the field-dependent thermopower of such systems to the mixed valence and empty orbital regimes, and carry out calculations in order to address a recent experiment on the field-dependent thermoelectric response of Kondo-correlated quantum dots [A. Svilans et al., Phys. Rev. Lett. 121, 206801 (2018)]. In addition to the sign changes in the thermopower at temperatures T-1(B) and T-2(B) (present also for B = 0) in the Kondo regime, an additional sign change was found [T. A. Costi, Phys. Rev. B (to be published)] at a temperature T-0(B) < T-1(B) < T-2(B) for fields exceeding a gate-voltage-dependent value B-0, where B-0 is comparable to, but larger than, the field B at which the Kondo resonance splits. We describe the evolution of the Kondo-induced sign changes in the thermopower at temperatures T-0(B), T-1(B), and T-2(B) with magnetic field and gate voltage from the Kondo regime to the mixed valence and empty orbital regimes and show that these temperatures merge to the single temperature T-0(B) upon entry into the mixed valence regime. By carrying out detailed numerical renormalization group calculations for the above quantities, using appropriate experimental parameters, we address a recent experiment which measures the field-dependent thermoelectric response of InAs quantum dots exhibiting the Kondo effect [A. Svilans et al., Phys. Rev. Lett. 121, 206801 (2018)]. This allows us to understand the overall trends in the measured field- and temperature-dependent thermoelectric response as a function of gate voltage. In addition, we determine which signatures of the Kondo effect [sign changes at T-0(B), T-1(B), and T-2(B)] have been observed in this experiment, and find that while the Kondo-induced signature at T-1(B) is indeed measured in the data, the signature at T-0(B) can only be observed by carrying out further measurements at a lower temperature. In addition, the less interesting (high-temperature) signature at T-2(B) greater than or similar to Gamma, where Gamma is the electron tunneling rate onto the dot, is found to lie above the highest temperature in the experiment, and was therefore not accessed. Our calculations provide a useful framework for interpreting future experiments on direct measurements of the thermopower of Kondo-correlated quantum dots in the presence of finite magnetic fields, e.g., by extending zero-field measurements of the thermopower [B. Dutta et al., Nano Lett. 19, 506 (2019).] to finite magnetic fields.
